Verse 1 of this chapter says that the sinner can still be delivered.
59:1 Look, the Lord’s hand is not too weak to deliver you;
his ear is not too deaf to hear you.
The word for deliver comes from yasha which means "be liberated," "saved," or "placed in freedom" (Isaiah 30:15; Jeremiah 4:14). Yasha' may also be used for "victory" in such places as Zechariah 9:9 or Deuteronomy 33:29, where the Israelites are called "a people victorious in Yahweh."
In this verse, the verb appears in the Hiphil stem. In the Hiphil, it is usually translated by such words as "deliver" and "liberate." The word is used for deliverance from physical strife (i.e. Isaiah 19:20; Exodus 14:30) and also moral troubles, though the latter is mostly in the prophets such as Ezekiel 37:23 and 36:29. Finally, it is used in lesser occasions as "give victory to" (Job 40:14; Judges 7:2).1
The term is almost always theological with YHWH as the subject and the people of God as the object (see Exodus 2:17 for an exception on both counts). While a few people are named as saviors (Judges 3:9, 15; 2:16; etc.), the object of salvation is never YHWH.
While the historical books consistently use yasha' to refer to physical well-being, the term takes on heavier, theological meaning in the prophets. The prophets would understand a more important part of salvation was spiritual. Indeed, sin was the ultimate enemy to be overcome! Not once in a prophetic passage is the savior other than God. Ezekiel 37:23 shows salvation to be spiritual. Likewise, Jeremiah 17:14 likens salvation to healing, and Isaiah 51:8 parallels the Lord’s salvation to His righteousness.
Important items to note are from Judges 6:31, that only a god who can save is worthy of worship, and that God is faithful and cares about his people (unlike other gods of antiquity). Also Deuteronomy 7:7ff shows that God saves because He loves.
The Septuagint often uses sozo and soter to translate yasha'. Sozo (the Greek term closest to yasha') in the New Testament may refer to physical security (Matthew 8:25; 9:21) but more often it will refer to spiritual salvation wrought by Christ (John 3:17; Romans 5:9; 1 Corinthians 15:2; etc.). The journey started by the prophets was completed in Jesus, and John would say "we have seen and do testify that the Father sent the Son [to be] the Saviour of the world" (1 John 4:14).
The problem in Isaiah 59:2 is not that these people cannot be saved but that they prefer their sins to being delivered. Later in this chapter, the people confess their sins and their need for God to deliver them (see Isaiah 59:9-15, especially 13). In verses 16-20, God first intervenes, then promises redemption to those who repent. Verse 21 says,
"As for me, this is my promise to them," says the Lord. "My spirit,
who is upon you, and my words, which I have placed in your mouth, will
not depart from your mouth or from the mouths of your children and
descendants from this time forward," says the Lord.
Looking at verse 20, we see that the "them" he refers to is the repentant.
1 Brown, Driver, and Briggs, A Hebrew and English Lexicon of the Old Testament, s.v. "yasha'" (Great Britain: Claredon Press, 1972 reprint), 446-447.