Are you having the same problem on the other devices that you have connected to that Sync account?

Or just the device that you updated from OS X 10.6 (Snow Leopard) to 10.11 (El Capitan)?

I don't have any other devices, just the OS X laptop.

Sync isn't intended to be used with one device. No tabs to be synced with no other devices on that Sync account.

Synced Tabs is for Show tabs from other devices. Hover over the Synced Tabs button and you'll that wording appear in the tooltip.

Interesting, thanks. So it was just a lucky break that it saved my tabs before, even though I was still only using the one device? (It was a lifesaver in dealing with a mysterious bug that would crash and refresh Firefox at random.) Or is there a way that it ought to still work?

Firefox automatically saves open Tabs when Firefox is closed, but that has nothing to do with Sync but rather with the Session Restore feature.

https://support.mozilla.org/en-US/kb/how-do-i-restore-my-tabs-last-time

https://support.mozilla.org/en-US/kb/restore-previous-session

Thanks. If that's the case, then it's odd that my tabs would, in fact, show up in Synced Tabs before. I definitely found it useful, given that my mysterious Firefox bug seemed to include wiping my Session Restore info as well.

(Incidentally, the same history/tabs/preferences-wiping random-refresh problem has happened at least once since I upgraded to OS X 10.11.6. I've never had this problem with Firefox on any other machine.)