It usually happens after I middle click on something (equivalent to "Open Link In New Tab"). Sometimes it happens immediately. For example:
1) I go to the website (I am logged in)
2) Middle click on a video thumbnail
3) The new tab from step 2 has a login page instead of the expected video
4) I log in
5) After successfully logging in, it redirects me to the home page instead of the video. I am now logged in (again).
6) So I go back to the first tab and try middle clicking on the same video thumbnail again
7) Then a new tab opens but instead of the expected video, it's the login page again. So apparently I'm logged out, even though only like 15 seconds passed since I logged in.
8) I have to log in again
Sometimes I have to login in several times in a row in a 2 minute period.
It is kind of random and doesn't always reproduce the same way all the time.
(You also did something to break middle click. Sometimes the first time you middle click on a video thumbnail, nothing happens. So you have to middle click twice.)
I am using a normal Chromium browser. I have cookies enabled. I am able to use other websites normally (including middle clicking on video thumbnails), so it would seem to be a problem with your website.
It is very irritating.