If NetworkManager stops your network stops, period. Firefox, Evolution and Empathy for sure depend on it and eventually everything will. You can frob an undocumented option on Firefox's about:config screen but no known fix exists for the others.
Solution: Troubleshoot your NetworkManager problem. It isn't optional anymore. Whether that is wise is a question best left to the philosophers.
of course, to troubleshoot nm, it's best to update the system first ...