If I understand the question correctly, it is the apparent contradiction between
A) Heb 10.14: For by one offering he hath perfected for ever them that are sanctified (KJV)
which offering was the cross - clearly a one-time event.
B) Rom 8.34, Heb 7.25, 1 John 2.1, which suggest an ongoing action of intercession that in addition to being ongoing, appears to supplement the cross as some further assistance.
Whereas I will argue that B) is merely a special case of A), an unpacking of the depth of A), which we experience as we mature in Christ.
What is a sacrificial system
Man feels guilt, regret, concern for others, worry about the future, and so desires to approach God and bring offerings that unburden him.
These offerings are always given whenever the need is felt, and they are given according to a liturgy, even if we do not visit an actual temple to perform a formal liturgy. The one we interact with in the performance of these liturgies is the mediator. There is always a gift.
The Priesthood exists not so that the offerings would be given, but so that they would be accepted, as Abel's, rather than rejected as Cain's.
Note that the offering exists for the benefit of the offerer, not God. If the temple were to be torn down, in three days the congregation would resurrect some system of rituals and ceremonies to fulfill their need to give offerings, as we cannot live without giving offerings. If sheep could no longer be slaughtered, they would be replaced with payment of money, and if money could not be given, people would beat themselves or fast or do something so that they can present their offerings to God.
The missing liturgy
This was a big deal because Christianity had no sacrificial system other than the cross, which could not be directly experienced, and whose blessings cannot be inherited by good works or personal sacrifice. There was no physical temple. There was no animal sacrifice. No rituals. No official priesthood. On its surface, it appears that the core human need for religious practice cannot be met by first century Christianity.
Of course Christianity would rapidly reassemble versions of physical liturgies, but when Hebrews was written, it was with the eye of addressing this gap. All those verses about how superior Melchizedek is, were not written to convince unbelieving jews, but rather to argue that 1) Christianity did have a sacrificial system, and 2) It was superior to Levitical system, not for purposes of winning an argument, but so that Christians would give offerings properly.
The new liturgy
In this new liturgy, instead of killing a ram for a trespass offering, one sees that Christ has already paid their debt. And instead of killing a she-goat for a sin offering, one sees that the water and blood that flowed from Christ's side has purified them. Instead of a burnt offering, one sees that Christ is all of their life, and instead of a peace offering, one partakes of the body and blood of Christ that was given on the cross. Instead of the high priest interceding on Yom Kippur, one sees that Christ is interceding for us, as he cries out "Father forgive them, for they know not what they do" - and how could the Father deny this dying request?
But for such offerings to meet the deep emotional and spiritual needs of the offerer, it must come as a revelation of the cross that is grasped at an equally deep level. If it is just an intellectual exercise, then the need for giving offerings will remain unmet, and the best case scenario is that offerings will continue to be given, over and over. The worst case scenario is that private liturgies will be adopted (which is idolatry). Reading systematic theology texts is not going to help. Just telling someone that they are forgiven is insufficient.
Repeated offerings in the new liturgy
So the question of "why would someone need to keep going back to the cross for forgiveness?" is answered by the simple fact that they still feel guilt. And therefore there is a sin offering that still needs to be given. Thus they go back to the cross and and confess their sins and feel better. This process will continue until their comprehension of the cross penetrates sufficiently deeply that they understand that Christ is their true identity.
Therefore John says:
1 John 2:1–2 (KJV 1900)
My little children, these things write I unto you, that ye sin not.
And if any man sin, we have an advocate with the Father, Jesus Christ
the righteous: And he is the propitiation for our sins: and not for
ours only, but also for the sins of the whole world.
Now a spiritually mature person would know that they are the habitation of Christ, and Christ is without sin, therefore they cannot sin. Any sin committed in the body is not committed by their true self, as Paul says
Romans 7:17 (KJV 1900)
17 Now then it is no more I that do it, but sin that dwelleth in me.
Romans 7:25–8:2 (KJV 1900)
25 I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin. There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
Notice that Paul says he still serves the law of sin with the flesh, but nevertheless he is freed from the law of sin and death. That is, because Paul's identity is not in the flesh, but in the Spirit, he is free. There is no condemnation. Such a person is also extremely rare and for everyone else, they continue to need to give sin and trespass offerings as they are still in the "O what a wretched man am I" phase and not yet in the "there is no condemnation" phase of spiritual growth.
The author of Hebrews was frustrated with this constant need to keep going over Christ's atoning and redemptive work, and wanted to "move on to perfection" (Heb 6.1-2), that is, he wanted to move on to offering yourself as a living sacrifice in the burnt offering rather than continue to revisit the trespass and sin offerings. Paul was also frustrated in his letter to the Corinthians:
1 Corinthians 3:1–3 (KJV 1900)
And I, brethren, could not speak unto you as unto spiritual, but as
unto carnal, even as unto babes in Christ. 2 I have fed you with milk,
and not with meat: for hitherto ye were not able to bear it, neither
yet now are ye able. 3 For ye are yet carnal: for whereas there is
among you envying, and strife, and divisions, are ye not carnal, and
walk as men?
Those who are carnal are called "babes", because they are still walking after the flesh. They do not understand that their identity is Christ, and so they still need to keep giving guilt and trespass offerings, as their carnal mind condemns them. That will keep happening until they learn to ignore the carnal mind, at which point they will be walking in the spirit, with no condemnation and thus no need for more sin offerings.
Again, reading a theology text is not going to help.
This is why people need to keep giving sin and trespass offerings, so let's look at how mediation works in the new liturgy.
David declares that Christ "is a high priest forever of the order of Melchizedek" (Psalm 110.4). That word for forever is olam which could also be translated as "for all times". In other words, Christ is available for all times and places. This is reinforced by the description of Melchizedek in Hebrews 7 of a man with no future, no past. A timeless quality, where someone steps out of nowhere, performs one sacrifice, and it is sufficient for Abraham, the man of faith. This is made explicit in Heb 9:12 (KJV 1900):
12 Neither by the blood of goats and calves, but by his own blood he
entered in once into the holy place, having obtained eternal
redemption for us.
Eternity is where the Father dwells (Is. 57.15) -- it is not a long duration of time, but outside of creation. When Jesus was on the cross in Jerusalem, cataclysmic things were happening: The world was overcome. The devil was judged. Creation was reconciled to the creator, etc. Big Stuff.
The Big Stuff wasn't constrained to the flesh in Jerusalem, although it certainly happened on the cross in Jerusalem, it was also in God's temple in eternity. Creation was shaken, the blood was poured out, the lamb was put on the brazen altar, the incense was lit and the blood sprinkled, a figure parted the veil and made intercession, the living water flowed, the burning, the sweet savor, cleansing, reconciliation, atonement, mediation, fellowship, and acceptance. This and much more was happening during the crucifixion in God's eternal temple. Because the temple is eternal, it is accessible from any point in time in creation for those who have been given the grace to see it. This is the divine service in the Temple of God that Moses saw and then patterned the tabernacle and levitical priesthood on it with its various offerings and rituals.
Thus Melchizedek represents the service in the eternal temple in Heaven, of which the Levitical priesthood is an earthly copy, and therefore the priesthood of Melchizedek is greater and precedes the Levitical Priesthood, just as the cross is the source of all the Levitical offerings. We can call the service of Christ in the true temple as the divine service. It is glimpses of this divine service that constitute the offerings of believers described in Hebrews.
The Divine Service
Aspects of this divine service were seen by other prophets as well, they called it "the day of the Lord". Abraham saw it, as Christ said "Your father Abraham rejoiced to see my day: and he saw it, and was glad." Abraham wasn't given a crystal ball to see the future in Palestine, he was given grace to see the service of the cross in God's temple.
All of the days in creation in which it is possible to see this divine service are collectively called "Today", as in "Today, if you will hear his voice, harden not your rights".
This service - the cross in all of its fullness - is one offering. But from it you get the sin offering, and the trespass offering, and the burnt offering, and the peace offering, the red heifer (which allows the the temple of the living God to reside in dead flesh), the scapegoat (in which the high priest mediates for the people) -- and everything else. Paul calls this "the unsearchable riches of Christ".
The Cross as grace when we see lack
Now this service is available in all times and for all people whenever, by God's grace, they can also peer into eternity and see it -- and it is seen by faith.
But if Moses saw the offering of the cross, and someone else saw it, that doesn't mean Jesus was crucified twice. There aren't two offerings, or two events or one event happening over and over. It is the same service, with different aspects seen by different people as their needs change.
If in the flesh you see a problem and are in need of intercession, then in the spirit you can see Christ advocating. If in the world you are wracked by guilt and need purification, then in the spirit you can see the Christ as the scapegoat, etc. All these offerings are available by grace whenever one sees lack:
Thou hast put all things in subjection under his feet. For in that he
put all in subjection under him, he left nothing that is not put under
him. But now we see not yet all things put under him.
But we see Jesus, who was made a little lower than the angels for the
suffering of death, crowned with glory and honour; that he by the
grace of God should taste death for every man. Heb 2.8-9 KJV
But God does not see lack, he sees everything under Christ's feet already, and the believer perfected by the one offering.