I had a very similar issue, but LP logged me out every reboot and ocassionally also logged me out if I closed Firefox.
I checked all "auto logout settings". Nope, all unchecked.
I uninstalled and re-installled Lastpass via the Universal instaler. Nope, still kept logging me out.
Disabled all my Firefox extensions. Nope, still kept logging me out. (I can see why it's frustrating to test this if you don't have Steps To Reproduce like I did by simply restarting).
The only fix that worked, now on two totally different systems (same Firefox & LP profiles, though) that exhibited the exact same issue: Reinstall Firefox. I know seemingly simple, but wham, bam, shazam!
Logged in and it hasn't logged me out yet even after reboots and closing Firefox. Someone else mentioned this, but I wanted to include the failed additional steps I'd taken.