I'm not posting any code, but can if anyone believes it's relevant. But the symptoms don't seem to point to the page or the code.
We have configured a Digital Experience. For the experience, we have created a single Visualforce page. The guest profile has been given access to the page and the page's controller. We have assigned that page as the "Active Site Homepage". The site will work as planned, meaning that when going to the base site URL or directly to the page, it will load without authentication. After a given amount of time (which we are not sure how long at this point) of the site not being accessed, when attempting to access the site, it will require authentication.
When that happens we try to troubleshoot. For example, I commented out some of the code on the page that was loading a Visualforce component. Tried loading the page, but it still took me to the login page. So I removed my comments, setting the page back to normal. Suddenly the page starts working and is accessible to everyone, from any location. Even for people who have never logged into the backend org. The page will continue to work for the rest of the day. The next morning we are back to square 1 and the site is requiring authentication.
I thought maybe it was the proxy caching by Salesforce, so I told everyone to stay out of the experience and waited 30 minutes. Since Salesforce says the caching is 10 minutes. But when I went to the page it worked without requiring authentication and I'm pretty sure that tomorrow morning it will start asking for authentication again.
The biggest issue is that we can't seem to troubleshoot. I will make a change to try and see what is happening and sometimes that change will cause the page to work, but then immediately reversing that change doesn't cause the page to break.
Has anyone else experienced this behavior before?