I would suspect a browser settings. Do you allow 3rd party cookies? I have "Block third-party cookies in Incognito" checked, but I allow all other cookies. However, I never actually run in the "Incognito" mode.
Currently I have three browser windows open, with greater than 20 tabs open in each browser window. I run like this all the time and have no issues with easily getting in and out of eHam, QRZ, or any other site.
The only issue I have is that, the "post" links in the eHam forums goes away, after about a week of connecting this way. It shows that I am logged in, but I can't post. A quick log out and log in fixes the issue for another week. I just had this issue when trying to post to this thread.