Having experienced being repeatedly logged out, I think I've found what the problem may be, at least for some. The site only wants to log in while on https, for me, but the header link, and possibly other links elsewhere, go to normal http and lead to the appearance of not being logged in anymore. In the limited testing I've done tonight, manually going to the address bar and making it https fixes it.
Even mid-post just now I've tested it. Click the head-case banner in a new tab, I show as not logged in. Add https:// on the address bar in that new tab, then I am logged in.