If you assume that Gragg felt the Fitzgerald situation was much ado about nothing (as a black man who played football in the SEC years ago, its likely went thru worse and heard about much worse)
He presumably felt that his advice to Schill was appropriate, that the timing around his planned trip to Europe was at his request - there was that email from Gragg to Fitz saying, almost apologetically, "Schill wants you to take a hit for this"
In other words it seems likely enough that Gragg is thinking - "I'm not leaving, Schill's the one who effed this whole thing up and if I resign it looks bad for me" (and of course he had no offers).
Not defending him as athletic director, just trying to piece things together.