Thanks for the link to the Cookie issues page. I've checked our configuration against that, and all seems correct. Our board is within a folder in the site - as per Example 1 on that page - details below.
The only change we made to cookie settings recently was to enable Cookie Secure when we switched to https last week, other than that we have had the same settings for ages with no issues.
Here's our board & cookie settings:
Board URL: https://catchat.org/felineforum/
Cookie domain: .catchat.org (with the dot at the beginning)
Cookie name: (we have used an unusual 12 digit cookie name here)
Cookie path: /
Cookie Secure: as the board is using SSL, this is set to 'enabled'.
Would it help to change the cookie name? Is it possible that users just need to clear their browser cookies? (just thinking if their browser loaded it before we switched to "cookie secure" - could that cause a problem if they don't refresh / clear cookies and it might sort the issue if they load a fresh cookie? (just thinking aloud, I don't really know enough to know if that would help or not).
Thank you for any further clues!