Which coaches?
Weber got fired because he missed 3 of 5 tournaments after inheriting the roster from one of those very rare stretches where we made 4 of 5 S16's. He'd gone 7 years in a row without a S16 before we fired him, after inheriting the Dee/Deron group.
Groce got fired because he missed four straight tournaments.
Both guys would've almost certainly gotten at least one more year had they made the tournament in their last season, even if they lost in the first round.
Those are the only two coaches we've fired in my life. Both for missing the tournament more often than they made it, not for losing in the second round.
Note the quoted material. I can't speak for who doesn't post here, but there are fans who say straight out that Weber needed to build on the early success.
Do you really think Groce would have saved himself by squeaking into the tournament with a 7-10 seed and then losing? Doubtful. He needed more than that.
The other people I'm thinking of -- Henson, Kruger, Self -- all had cited other reasons for why they left. But all three ended up coaching somewhere else again in college down the road. I doubt that the pressure to WINWINWIN can be discarded. Do we really think that if Self had made the Final Four in 2001, defeated Kansas in 2002, and then made another run in a loaded regional in 2003 that Illinois would have hesitated to at least try to match the offer he ended up getting?