Start Firefox in Safe Mode {web Link} by holding down the <Shift>
(Mac=Options) key, and then starting Firefox. A small dialog should appear. Click Start In Safe Mode (not Refresh).

Is the problem still there?

I will have to try Safe Mode later. Since the sync this morning logins are there even after a computer reboot.

Issue back this morning. Safe mode does not resolve. Menu had ?message icon. (Triangle with !) Message was to reconnect.

 This may be a sync issue. Not staying logged in.  Also,  Manage Account - Devices - shows multiple instances of my Office PC.  
 Maybe stopping all sync and removing my IOS device and the multiple instances of the PC?  Syncing with my iPad is not critical, just nice.

If you have sync, and there is a problem anywhere, Shut Down Sync Immediately On All Devices to prevent the problem from spreading. Once the problem is fixed, perform the same repair on all computers before using sync again.

I called for more help

These can't get your data back but will help in the future.

These add-ons can be a great help by backing up and restoring Firefox

FEBE (Firefox Environment Backup Extension) {web link} FEBE allows you to quickly and easily backup your Firefox extensions, history, passwords, and more. In fact, it goes beyond just backing up -- It will actually rebuild your saved files individually into installable .xpi files. It will also make backups of files that you choose.

OPIE {web link} Import/Export extension preferences

I ran sync on PC to retrieve all logons then disabled sync on both devices. I also downloaded the FEBE add-on. Better safe than sorry. Thank you for your further investigation.

Watch and see if this happens again, and report it here.

FEBE: Click the arrow next to the icon. Select Restore and select what you want.

This morning, sync still off and all saved logins are gone. FEBE had not backed up. I signed in to Firefox and logins returned. Did a manual FEBE backup. Have not turned off sync again as this may not be the problem after all.

FEBE, like many programs, has to be set up thru its options.

https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.