I have an LTZ that I ordered with the 60/40 bench seats. Your issue may not be the same as mine was as I'm not real familiar with the captains chairs but it could be the same thing or something similiar. I also don't know if you mean the seatback won't fold down or the seat won't fold forward (tumble) against the front seat back.
My "60" side would not tumble against the front seat at times because the latch would not release from the square ring in the floor (the seat folds and tumbles because it is spring loaded after releasing). I could use the handle but it was very stiff. I also had to really slam it down hard for the latch to catch on both sides. If both latches don't catch you cannot raise the seatback. At least on my bench seat.
I lowered the seat without slamming and with the seatback down pushed down on each back corner of the seat and found that the side of the seat near the door would move up and down a little which told me this latch was the one that was not catching and locking. I removed the molded carpet pieces and loosened the mounting plate nuts and put a metal shim under the mounting plate where the square ring was that the seat latch hooks into and tightened the nuts back. This deformed the mounting plate slightly which raised the ring a little. Now the seat latches onto both rings the same and I don't have to slam it down and the power fold and tumble works everytime. I don't know if the seat was twisted or the floor under the mounting plate was off a little but this fixed the problem.