In short, there seem to be many manuscript variants that remove mention of multiple crowings, in 14:30, and in the fulfillment sections of 14:68 and 14:72. THGNT's theory, which strikes me as fairly reasonable, is that what we have is attempted harmonization with Matthew and Luke (and John) through omission.
However, I think there is more to it. "Second cockcrow" seems to have had a technical meaning, for both Greek and Latin authors. Here is Erasmus.
If Mark 14:30 is a statement about a particular time of day, then the mentions of a second crow at 14:68, 72 become a blunder. This blunder would be on the same order as Matthew's misinterpretation of Zechariah 9:9 at Matthew 27:7. Mentions of a second crow at 68 or 72 over-literalize a technical/poetic statement about the time. (A single crow call, alerting Peter to his forgotten promise, is not a blunder, but makes perfect narrative sense.)Sed ut ad interpretationem adagii recurramus, veteres initium diei a prima mediae noctis inclinatione ordiebantur, proximum tempus gallicinium vocabant, quod id temporis lucem multo ante praesentientes incipiunt canere; tertium conticinium, cum et galli conticescunt et homines etiam tum quiescunt; quartum diluculum, cum incipit dignosci dies. Quintum mane, cum clarus iam dies exorto sole. Itaque secundus gallorum cantus multo solis exortum antevenit. Hinc Iuvenalis:
Quod tamen ad galli cantum facit ille secundi,
Proximus ante diem caupo sciet.
Consimiliter Aristophanes in Contionatricibus:
Οὐδ’ εἰ μὰ Δία τότ’ ἦλθες, ὅτε τὸ δεύτερον
Ἀλεκτρυὼν ἐφθέγγετο, id est
Ne si quidem illo te appulisses tempore,
Cum gallus iterum caneret.
Huius rei mentio fit et in evangelicis litteris.
So who made the blunder? Given that Matthew/Luke/John have no mention of a second crow, and given the manuscript confusion, I would blame copyists reading Mark 14:30 and trying to (over-)harmonize Mark with itself. The harmonization attempt bounces around between the two verses because of original copies that contained no second cock crow at either 14:68 or 14:72.