GREATLY depends on where you hit the deer. There is no rule of thumb. A lot depends on examining the arrow and analyzing the deer after it was hit and being able to follow the flight of the arrow and seeing where it was hit, replaying the shot in your mind and being attentive to if it was a solid good hit. Listening to the sound of impact, what kind of blood you have, etc...

Double lung: die within sight or IMO 1-2 hours (deer aint going anywhere if he's dead better safe than sorry)
Hear: ditto
Single lung: 4 hours at least and deer can still travel a long way
Liver: 4-6 hours
Gut: go home and get some rest and some buddies and come back in 8 hours and search like heck.