I have a feeling that Gilmore was unfairly labeled as a "loser" primarily because Virginia's one-term governor law means that the subsequent governor needs to be from your party for anyone to be labeled a "winner". Gilmore stood up for his principles, perhaps to the detriment of the politics involved in getting Earley elected governor. That error (if it can be called an error) may have led to the perception in the higher-ups that he appeared weak as a GOP leader. So I think it likely that he was asked, no doubt politely, to evaluate whether or not his continued role as GOP chairman was in the best interests of the party.
I have a feeling, like others here, that Karl Rove may become the GOP chairman for the 2002 battles.