Why is the drywall in my garage sagging?
The problem is because sheetrock does weaken a little over time, and with moisture, but the reason you are seeing it sounds like you just haven't used enough fixing points.

Usually you would fix to joists no more than 24" apart, and separate your screws on each joist by 16", which gives you a structure which can even cope with small amounts of water leakage without damage .

If you have joists already present, then you may be able to push the sheetrock back up and nail it correctly, however it may already be permanently warped - this will depend on just how far the bowing is.

I would guess though, that you don't have joists at that spacing - otherwise the sheetrock would probably be fixed to it already - so you will want to remove it all, fix joists and use new sheetrock. (This will be a fun job - especially if the existing stuff is a bit damp - bring friends to help bring it down otherwise you will have an exceedingly messy afternoon)