Not get second chances at big name programs. Everyone makes mistakes. I see Tuberville, Nutt, Petrino (assuming he will be sought after soon) get good job after good job. I even wondered why Hammy hasn't popped up on some schools AD radar.
Zook was the head coach at Illinois for a few years after he left Florida. He did okay for a while, but later was let go again. Dooley will have to work his way back up to be a head coach if he is able and wants to. Fulmer is another story.
I would take a guess that other teams took a look at the direction that the U.T. headed after Cutcliffe left, came back, and left again. They may have decided that Cutcliffe was the glue that held it together. I remember reading that the work ethic of the staff and players went down when Cut left both times.
Most of Fulmer's success came when the only top coaches in the SEC were Spurrier at Florida, and Gene Stallings was at Alabama for a very few years. Fulmer had little success against either. After Stallings left, Fulmer was able to beat Shula and Dubose at Alabama. Fulmer couldn't beat Spurrier with any regularity, and couldn't beat Saban at LSU or the one time at Alabama.
He made his name against Goff, Donnan, Scott, Widenhofer, McIntyre, Curry, Mumme, DiNardo, etc. There was really only one other good team in the East, and that was Florida.
The other possibility is that Fulmer was offered something like a rebuilding job, and his ego wouldn't let him take a lesser job, or that he was afraid that he would go out a big loser, and tarnish his reputation. Remember, Fulmer never had to rebuild a program. he walked into a great job.
I will give him credit for keeping the program at a high level for several years, but it went down gradually, then crashed, after the first 9 or 10, after SEC teams got better coaches..