I frequently connect to other networks through VPN. It is the case that when I actually connect to another network via VPN, Firefox doesn't pick up the new network settings. Some networks require a proxy and some don't. When Firefox included the option "Use system proxy settings" in Connection Settings, I was excited for this feature but it doesn't appear to work. Unlike Internet Explorer and Chrome, which picks up the correct network settings upon network change without restarting, Firefox requires a restart.
Bug filed at https://bugzilla.mozilla.org/show_bug.cgi?id=563169