Here, on Arch, Firefox updates don't cause me any grief. Only time I've ever need to reboot is after a kernel or DKMS module update.
For systemd updates, I can just reload it. For the likes of core components like bash, and major DE updates, I can just lazily use loginctl to terminate all of my sessions, and start fresh.
I'm not sure why Firefox would be causing instability until you restart (reboot?), though.