I use FF on Mac OS and have never seen it refuse to operate due to an update. It will sometimes popup a dialog letting me know there is an update but I can dismiss it. I tend to check for updates every couple of weeks, anyway. The update process is mostly painless though it does restart the browser. That is probably a good thing anyway. Most updates I get when I do update the browser for other reasons and it installs and update as it is restarting.

That sounds truly horrible. I've only recently returned to Mac OS as primary OS (one reason being annoyed by Ubuntu and FF) but why aren't you using Safari and Mail.app then if I may ask?