Is this all mediated by "remembering logon?"
I don't know. I always have it on because I am in and out of the forum sometimes dozens of times a day!

Does "Auto-save"stop annunciating when one has been silently disconnected?
It shouldn't, but it depends on cookies so if your browser is set to dump cookies or whatever that context will be lost. Normally it will work as you found.

However, when that first blank screen appears after re-logging in, it is pointing to a page something like this

https://forums.dc3.com/newreply.php?do=postreply&t=13041

This leads nowhere.
I'm not sure about that. If I refresh from an incomplete post, it comes right back to the (empty) Quick Reply form with the Restore button in the lower left. Even if you go back to the main page and drill back down to the post to which you were replying, the restore button should appear as you found. It does work pretty well. Like you, though, when I am making a really complicated one that may take me over a half hour (and I do that more often than pone might think) I''ll prepare it offline in Notepad++.