Gregg,

You had written:

"There are some believers that believe the apostasy of the church comes when those who miss the Rapture, having taken the mark of the beast rather than die for Christ. This event most likely will take place sometime toward the end of the tribulation period.  Obviously those who believe this apostasy comes after the Rapture believe it is still to come, but what does scripture teach?" 

There are different teachings about that:

II Thessalonians 2:3 ¶ Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;

          In summary, there are three different views held on II Thessalonians 2:3, by PreTrib-Rapture advocates:
1)      Both the falling away and the revealing of the man of sin occur after the rapture in the tribulation
2)      Both the falling away and the revealing of the man of sin occur before the rapture, before the tribulation
3)      The falling away occurs before the rapture and the revealing of the man of sin occurs after the rapture in the tribulation

The three different interpretations of II Thessalonians 2:3.

II Thessalonians 2:3 Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;

1)      The one say “that day”, points back to II Thessalonians 2:2
II Thessalonians 2:2 That ye be not soon shaken in mind, or be troubled, neither by spirit, nor by word, nor by letter as from us, as that the day of Christ is at hand.
That is referring to the 2nd Advent at Armageddon, so that the falling away & the initial revealing of the man of sin both occur completely within the Tribulation, after the blessed hope (rapture)

2)      Another say “that day”, points back to II Thessalonians 2: 2, as well
II Thessalonians 2:2 That ye be not soon shaken in mind, or be troubled, neither by spirit, nor by word, nor by letter as from us, as that the day of Christ is at hand.
And that “the day of Christ” points back to II Thessalonians 2:1

II Thessalonians 2:1 Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and by our gathering together unto him,
Which is speaking about the blessed hope (rapture), that he expounded upon in I Thessalonians 4:13-18.
This then would have:

i) “the day of Christ” refer to the blessed hope,
ii) so that first there would be the falling away,
iii) then the man of sin revealed,
iv) and then right after that comes the blessed hope,
v) followed by the seven years of Daniel’s 70th week

3)      The third view is that verse three reads as follows"

a.      The “falling away” (apostasy)
b.      The “comma” in the verse, representing the rapture
c.       Then begins Daniel’s 70th week, when the man of sin is revealed

Gino