Since you said it's a rental, I'd start by calling the landlord. It's their lock, it's their property, it's their responsibility to fix it (or to authorize you to get it fixed and deduct the cost from your next rent check, or something of that sort).
If you want to try doing something yourself: Dismount the thumbturn and lock cylinder. Looking into the resulting bore through the door, you'll be able to see the deadbolt's mechanism. Try turning its hub with a screwdriver and watch it move. I'm betting you'll see part of the linkage banging into the surrounding wood, and that if you remove a bit of wood there for the linkage to operate it'll solve your problem. (Uncommon but not unheard-of problem; wood shrinks as air humidity decreases, and sometimes things shift enough that a hole bored in midsummer won't quite align well enough in midwinter.)
The other (less likely) possibility is that the bolt mechanism is broken. In which case you'll have to figure out how to retract it, since you can't replace it until you can open the door.
HOWEVER: If the bolt mechanism appears to operate normally with the thumbturn and cylinder removed, the issue is probably one of "timing". There is a limited range of free motion designed into the linkage between lock, bolt mechanism, and thumbturn; this is what allows the lock or thumbturn to retract the bolt without the other turning. The parts need to be installed in such a way that this freedom is at the right point in the locking/unlocking cycle; if you get that wrong, that can produce exactly the symptoms you're seeing where the key or thumbturn stops before it can retract the bolt. The solution in that case is to reassemble these parts correctly aligned, which is a bit of a pain to describe in text and which varies a bit from lock to lock. If you can tell us what brand of lock it is, we may be able to talk you through that.