Edit: The problem seems to be cured. I usually use a link on my Bookmarks Toolbar that I created some time ago, that does a search for new posts, vs opens the forum directory. I just replaced that link with the link for new posts that appears in the "Quick links" shortcut at the top left of the forum page, and now it doesn't prompt for a login each visit.
I think the original link was "https://www.data-medics.com/forum/search.php?search_id=newposts&sid=75d1ba133e041533d5bf4bc84973225c"
and the new link is "https://www.data-medics.com/forum/search.php?search_id=newposts." Looking at yesterday's browser history, the links were similar to the first I mentioned, but had slightly different SID's, so maybe that was at the root of the problem. Anyway, it's fixed now.