How to solve apparent issue with cookies not being saved on Safari Version 16.4.1 (macOS Big Sur) - constantly needing to re-sign in

I am a member of an online forum and have been experiencing constant log outs upon first opening the saved page for that forum, which for years has seamlessly filled in my user name and password and allowed me to enter the site without problem. Now, although I'm first presented with what looks like a normal page, when I click on anything, I get a messages saying I've been logged out and I have to log in again. Once I do that, it's good for the rest of a session. This has been going on for more than a week, and the tech people at that forum have determine that the problem appears to be related to the recent update to Safari (to 16.4.1) rather than being on their end. I'm now trying to figure out how to downgrade to the previous version, but first would like to know when this problem will be solved. Thank you.