It seems to be some hide script on your navigator, try to open the levelextreme.com in incognito mode to prevent the issue and/or using other navigator for a while to see if the problem appears again. This will let you know what is going on.
Are you leaving opened the site for days and days? maybe that is also the problem, I never kept opened this site more than 2 consecutive days.

>I'm getting this several times a week, and I think it's been like this for a few months. Didn't run any statistics, assuming there's sufficient logging on the server. Happens usually while I'm away, when automatic refresh tries to reload the menu.

See the image.