It's been more than a month since the last occurrence, so I'll go out on a limb and guess that Safari 12 has fixed whatever was wrong.
The second tech had even more trouble understanding my problem and kicked me upstairs to a Senior Adviser who, when he finally understood it, did some research and advised me that what I've experienced is expected behavior that Apple began implementing in Sierra and fully implemented in High Sierra.
Apparently, there's a cookie somewhere that periodically causes the "Never Saved" info in Safari > Prefs > Passwords and your keychain to be wiped, the purpose of the exercise being to remind you that your password isn't saved and give you a new opportunity to save it.
Based on what I was told, everyone who has "Never Saved" passwords should be experiencing what I've reported.
Well, so much for that; it never did make much sense, anyhow!
