The double-edged sword at the beginning symbolizes salvation. It is double-edged because the Word may be rejected. The Word of salvation cuts "both ways." Thus, the (single-edged) sword at the end is a different instrument. After the heavenly celebration of salvation, those "on the outside" war against the judgement the Word of God must finally bring.
The Type of Sword
The English translation of "sword" throughout Revelation masks the original language. John employs two types of swords: ῥομφαία, rhomphaia (of this question), and μάχαιρα, machaira. The physical difference is size. A machaira is a large knife or small sword. A rhomphaia is larger. Describing either as "double-edged" is unusual as they normally would have a single edge.
Machaira is the common New Testament word (29 times). Outside of Revelation rhomphaia is used once in Luke (2:35) and it is never placed in man's possession. John uses both types in Revelation. He begins with a description which is at odds with their regular appearance:
Type Characteristic Possession
1:16 rhomphaia sharp two-edged Christ - Mouth
2:12 rhomphaia sharp two-edged [Christ - Mouth]
2:16 rhomphaia --- Christ - Mouth
6:4 machaira great Rider of the red horse
6:8 rhomphaia --- Death
13:10 macharia --- Beast/men
13:10 macharia --- Beast/men
13:14 machaira --- Not specified
19:15 rhomphaia sharp The Word of God - Mouth
19:21 rhomphaia --- The Word of God - Mouth
After their atypical characteristics, each ends correctly described. With the exception of 6:8 the rhomphaia is associated with Christ and is placed in the mouth and/or called the Word of God.
Machaira is never connected with Christ (but may refer to "word" in chapter 13). The exceptional use of rhomphaia in 6:8 has no mention of word or mouth. Here only is the use typical of the Old Testament message of judgement (see below). This "sword" follows a similar use of machaira:
And out came another horse, bright red. Its rider was permitted to take peace from the earth, so that people should slay one another, and he was given a great sword (machaira). (6:4) [ESV]
And I looked, and behold, a pale horse! And its rider's name was Death, and Hades followed him. And they were given authority over a fourth of the earth, to kill with sword (rhomphaia) and with famine and with pestilence and by wild beasts of the earth. (6:8)
When considered together, John's description of the macharia as μέγας, (megas) creates a continuum of two large swords, both which bring death to the earth. As both swords normally have a single blade, the two riders bring death by the edge of two swords, a type of double-edged use.
John's use of μέγας to describe the machaira echoes the LXX description of two great lights in Genesis (1:16). Just as God made two great lights to give light to the earth; John envisions two large swords which bring destruction:
great light greater light
red horse pale horse
megas machaira rhomphaia
destruction greater destruction
The specific megas machaira may have been taken from Jeremiah 25:38 (some versions) or Isaiah 27:1 in the LXX; a double-edge (δίστομος) rhomphaia is found only in Psalm 149 (see below).
The Symbolic Use Rhomphaia
In his commentary Gerald L. Stevens says the rhomphaia is used in a war of words:
Mouth: sharp, two-edged sword (1:16), martial imagery allusive of war, but "out of the mouth" means not a normal war. Rather, this is a war of words, of witness and testimony. Sword imagery in biblical contexts normally implies a word of judgement.
47 John uses martial imagery throughout Revelation, but some interpreters do not pick up that John's rhetoric is subversive.
48 This sword is not in the hand, as in normal warfare. Rather, this sword is out of the mouth, which makes all attempts to represent this artistically somewhat clumsy.
The only weapon in this war is words. Isaiah confirms this way of framing the conflict, as the expected Davidic ruler will "strike the earth with the rod of his mouth" and will vanquish the wicked "with the breath of his lips" (Isa 11:4 NRSV)
49 This conflict is of witness and testimony, the claims of Caesar versus the claims of Christ. The sword coming out of the mouth of the Son of Man is the theological equivalent of Jesus' penetrating question to his disciples in Mark 8:29 - "Who do you say that I am" - now addressed to believers in late first-century Asia Minor. John's sword has two characteristics. Being sharp, the sword cuts through anything, including Roman imperial propaganda, as in Virgil's almost euphoric celebration of the world Augustus created as savior and peacemaker.
50 Being two-edged, the sword cuts two ways, negatively as judgement, but positively as salvation.
51 John's uses here echoes that in Hebrews, "For the Word of God is living and active and sharper than any two-edged sword, and piercing even as far as the division of soul and spirit, of both joints and marrow, and able to judge the thoughts and intentions of the heart" (Heb 4:12). With this "sword out of the mouth" imagery in the Inaugural Vision of the Son of Man, we can read ahead to be sure we make the connection John intended with the rider on the white horse in Rev 19. Note that this rider "judges and makes war" (Rev 19:11), but he is entitled the "Word of God" (19:13)...this warrior is given the description "from his mouth comes a sharp sword" (Rev 19:15), which is how those defeated are slain "by the sword of the rider on the horse, the sword that came from his mouth" (Rev 19:21).
Stevens does not comment on why the two-edged sword is not described as such later. However, as he notes, a double-edged sword cuts both ways, negatively in judgement and positively in salvation. In this case, one side would be symbolic of judgement and the other of salvation.
As Stevens notes, "double-sided" recalls Hebrews 4:12. However, John replaces the machaira of Hebrews with rhomphaia. This exchange recalls the only NT use outside Revelation:
And Simeon blessed them and said to Mary his mother, “Behold, this child is appointed for the fall and rising of many in Israel, and for a sign that is opposed (and a sword [rhomphaia] will pierce through your own soul also), so that thoughts from many hearts may be revealed.” (Luke 2:34-35)
Following Luke, John's rhomphaia conveys the sense of judging. It is apparent John has been purposeful to maintain a distinction between rhomphaia and the machaira common to the NT (especially Hebrews and Ephesians 6:17). Thus, in the NT men have the "machaira of the Spirit" and proclaim the "word of God" which is sharper than any "two-edged machaira," but in Revelation only Christ possesses the rhomphaia Word of God.
This symbolic use of the double-edged sword represents the Gospel. The Word of God which is sent to bring salvation brings judgement if rejected. Commenting on John 5:24-27 Craig R. Koester says:
In positive terms, Jesus promised that anyone "who hears my word and believes him who sent me has eternal life; he does not come into judgement, but has passed from death to life" (5:24)...In negative terms, those who do not believe in him remain under divine judgement.
The symbolic progression from salvation to final judgement is apparent in the message to the church at Pergamum:
“And to the angel of the church in Pergamum write: ‘The words of him who has the sharp two-edged sword. (2:12) … Therefore repent. If not, I will come to you soon and war against them with the sword of my mouth. (2:16)
The sword is Christ's (1:16). He brings His "sharp double-edged" word: salvation or judgement. For those who fail to repent He will war against them with the (single-edged) sword of His mouth. The war threatened (2:16) comes later (19:21):
Sharp double-edged rhomphaia (1:16)
Sharp double-edged rhomphaia (2:12)------>[single-edge] rhomphaia (2:16)
[single-edge] rhomphaia (19:21)
Likely, John intends the reader to see two distinct instruments, the sharp two-edged rhomphaia of Christ intended for salvation which cuts "both ways" and the single-edged rhomphaia of the end.
Another Two-Edged (δίστομος) Rhomphaia
There is one use of double-edged rhomphaia in the LXX:
The devout will boast in glory, and they will rejoice on their beds. The exaltations of God are in their throat, and two-edged swords in their hands, to execute vengeance among the nations, rebukes among the peoples, to bind their kings with fetters and their nobles with iron handcuffs, to execute among them a judgement inscribed. This glory is for all his devout. (Psalm 149:5-9 NETS)
καυχήσονται ὅσιοι ἐν δόξῃ καὶ ἀγαλλιάσονται ἐπὶ τῶν κοιτῶν αὐτῶν αἱ ὑψώσεις τοῦ θεοῦ ἐν τῷ λάρυγγι αὐτῶν καὶ ῥομφαῗαι δίστομοι ἐν ταῗς χερσὶν αὐτῶν τοῦ ποιῆσαι ἐκδίκησιν ἐν τοῗς ἔθνεσιν ἐλεγμοὺς ἐν τοῗς λαοῗς τοῦ δῆσαι τοὺς βασιλεῗς αὐτῶν ἐν πέδαις καὶ τοὺς ἐνδόξους αὐτῶν ἐν χειροπέδαις σιδηραῗς τοῦ ποιῆσαι ἐν αὐτοῗς κρίμα ἔγγραπτον δόξα αὕτη ἐστὶν πᾶσι τοῗς ὁσίοις αὐτοῦ
Much of John's imagery can be seen as originating here. Devout people have the exaltations of God in their throat and the two-edged rhomphaia in their hands. John places the two-edged rhomphaia in the mouth of Christ to bring salvation which will result in unarmed people glorying in God, rejoicing, and proclaiming the exaltations of God.
Addendum - A Two-Edged Hebrew Word Sword Picture
The two-edged sword which is the Word of God, calls a reader to both Greek and Hebrew texts. In Hebrew, פֶּה is the word for both mouth and edge. דָּבָר is word but these same consonants also make דֶּבֶר, which is "pestilence" or "plague." So the "Word" in Hebrew from the mouth of God creates an interesting picture of a two-edged sword:
One side is the mouth bringing the Word. The other is the edge bringing pestilence, plague (6:8), and ultimately death.
3. Gerald L Stevens, Revelation, The Past and Future of John's Apocalypse, Pickwick Publications, 2014, pp. 271-272
4. Craig R. Koester, Symbolism in the Fourth Gospel, Meaning, Mystery, Community, Fortress Press, 1995, p. 88
47. Anthony T. Hanson, The Wrath of the Lamb, SPCK, 1957, pp. 166-167
48. CF. David L. Barr, "The Lamb Who Looks Like a Dragon? Characterizing Jesus in John's Apocalypse" pp. 205-206 in The Reality of Apocalypse: Rhetoric and Politics in the Book of Revelation. Edited by David L. Barr, SBLSymS, Num. 39. Edited by Christopher R. Matthews, Society of Biblical Literature, 2006.
49. Isaiah's imagery in Isa 11:4 and John's imagery in Rev 1:16 echoes in the unusual description of the lawless one in 2 Thess 2:8, "whom the Lord Jesus will destroy with the breath of his mouth."
50. Ecl. 4. Ferguson pointed out the "almost 'messianic' aura that surrounded the expectations of the people in the Augustan age," Backgrounds of Early Christianity, Erdmans, 2003, p. 114. CF. Horace, Satires, Epistles, and Ars poetica, Translated by H. Rushton Fairclough, LCL 194, Harvard University Press, 1926, 2.1.15; Andrew Perriman, The Coming of the Son of Man: New Testament Eschatology for an Emerging Church, Paternoster, 2005, p. 163
51. Cf. Mitchell G. Reddish, Revelation, Smyth & Helwys, 2001, p. 41