Not sure about Rex being defensible, but here are four reasons why I don't want to see a coaching change.
1) From an outside point of view (not crazy fans over analyzing everything) any team that burns through six coaches since 2008 is a hot mess. With obvious organizational issues, no sane coach would want to go into a meat grinder like that. Let the Pegula's establish some stability and "street cred" around the league. While the Bills are a huge disappointment, they have been a 500 team for the last three years, and sadly enough that is improvement from the previous 10 plus debacles.
2) It was silly to bring in a 3-4 coach to come in and coach a team whose strength was a 4-3 defense with no QB. We didn't have the players to run the 3-4. We have "some" now, so it's hard to tell if it's the players, the coach, or both at fault for the poor D.
3) Rex is not a great head coach- (see timeouts, schemes, gameplans, penalties etc) and only a great head coach can overcome the massive injuries we've had. Not an excuse, but it is a reason. Let this play out with a full hand.
4) No franchise QB. What are the Bills supposed to do with a guy like Tyrod?? Air it out? Ground and Pound is a must for now