How do I prevent just 'exit' from being saved when I close an SSH connection?

When searching for a way to do this on Google, all I can find are ways to quit the session without saving history (like kill -9 $$), but I have the opposite problem. I want to save all of my history, just not the exit command.

Comcast has really abused us at work such that our SSH tunnels can't stay up for more than 5 minutes without getting broken pipe. After reconnecting, I go to run the last command and sure enough, I forget it's now exit!