Generally speaking, you can get another FASTPASS starting 5 minutes after the beginning of your current FASTPASS's return window. In other words, if your return time is 10:00 - 11:00 a.m., it will probably say on the bottom that you can get another FASTPASS after 10:05 a.m.

If your return time is many hours from now, it will say you can get a FASTPASS 2 hours after you got the current one. So if it's 10:00 a.m. right now and your FASTPASS return window is 3:00 - 4:00 p.m., it will say at the bottom of your FASTPASS that you can get another one beginning at Noon.

Who knows, there might be some experimenting or beta-testing going on somewhere, but what I wrote above is the overall policy.