What changed my mind was a "Eureka!" moment while poring over Revelation 12 (see this). When I understood the imagery in that passage, it was as if I'd been given a key that unlocked everything else the Bible said about eschatology. Suddenly, just about everything fell into place, including the Olivet Discourse. As it did, I no longer disdained the Secret Rapture teaching, but found myself, to my surprise, accepting it and thereafter promoting it.
The mechanics of Jesus' return as detailed in the Olivet Discourse are the same regardless of which approach to the Rapture one takes. Astronomical wonders and some uniquely associative heavenly sign immediately precede the visible return of Christ through the clouds. The series of events will be absolutely unmistakable and inescapable, like lightning illumining the whole sky. As he comes through the clouds, he will gather his saints together from the four winds (all over earth) and from one end of heaven to the other.
Pre-tribbers and mid-tribbers assume at least some saints were already in heaven (i.e., raptured, not just the dead in Christ) when Jesus finally arrives on earth. The text explicitly states that he gathers his saints from from all over the heavens so that is certainly a valid perspective. How those on the earth are gathered is not intimated, it is only said that they are gathered in the lot. I see nothing in the text which implies that those on the earth are quickly whisked up into the air just to experience a meteoric descent back to earth immediately afterwards with Jesus.
Post-tribbers have to assume that very thing, the sequence as follows: Christ appears in the heavens, gathers the saints from heaven (the dead in Christ) and earth (those alive and remaining) in the air (necessitated by 1 Thessalonians 4:15-17) and then immediately returns to earth with them in tow.
Among other issues with that scenario, it does not jive with Revelation 19:19-20:5. That text clearly states that there are saints who did not take the mark of the Beast and that are raised from the dead (raptured, for all intents and purposes) in isolation from the rest of the dead. The passages that deal directly with the faithful dead being raised or raptured (1 Corinthians 15:50-52; 1 Thessalonians 4:13-17) clearly state that all the faithful dead at the time of the Rapture rise together. Therefore, the unmarked saints from the Tribulation cannot be part of the faithful dead at the time of the Rapture.
The only way the math works out is for those unmarked, Tribulation saints to die after the Rapture has occurred.
If those Tribulation saints must die during the Tribulation but after the Rapture, the post-tribulation perspective is untenable. The mid-tribulation perspective is not eliminated, not at least by the passage mentioned above. It does have issues with what follows in the Olivet Discourse (see this), however. It seems the escape of the Rapture, at least for the broadest measure of the Church, must happen suddenly in the midst of ordinary life, and hence pre-tribulationally, according to the scriptures.
I must admit my approach to the Rapture in the Olivet Discourse is not a slam dunk. The language Jesus used in these passages is ambivalent enough for anyone so determined to justify in their own mind seeing these passages in another light. I do believe my approach to the Revelation and Daniel is more than solid and that everything else fits together within my interpretative schema, whereas nothing does under a mid- or post-tribulational regimen. If either of those approaches are right, no worries, bad things will happen to awake the slumbering before Christ returns, and they won't be caught with their pants down.
If my approach is right, we need to be ready now.