That's definitely a good idea, and I think that only bad part about it would be overhead. Depending on your situation, re-opening SSH connections may not be an acceptable amount of load for the server.

On the other hand, closing the SSH connection would make your job a lot easier, as you wouldn't have to worry about sessions at all. It's definitely at least worth looking in to, coding your app without sessions would be a simple matter and would be a good development step in coding your app with sessions.