I don't use Fennec. But mull.
I hope you know about 'Clear Cache', and this issue is not that. If you haven't done that you can do a simple search to find steps.
If the clear cache did not solve the issue, the only way is backing up only relevant data. It looks like Fennec does support sync. In that case you can login using a mozilla account, and choose what to sync. Once all your stuff is synced with another device, its safe to do whatever you want.