Not rot, just dried out. When faced with this situation, I liberally apply Proof Hide, top and bottom, ensuring that I rub it in well. Liberal is an operative word. Once Proof Hide is applied, I put the saddle in a plastic bag and set it on a windowsill (indoors) that gets a lot of sun. Then I leave it there for a day or two.

The heat melts the Proof Hide allowing it to better penetrate the dried out leather. This is not a sure fix but it has worked for me, now and again...

Needless to say, you can repeat this procedure more than one time to get the best results.