I had this issue originally. There is no 'remember me' option on the main login page, so the site doesn't send a cookie or anything to keep you logged in. Here's the solution I found:
Enter an incorrect password on the main page
You will be redirected to a different login page
Enter the correct information and check the box to keep yourself signed in
After you do that, you should stay logged in until you either log out, or your browser deletes its history/cookies/saved logins. If that is the actual issue, I can walk you through fixing it better over teamspeak.
I have tried many times to correct this in the control panel for the site. It seems to be a bug in the system and there aren't any updates on the horizon. Just one of those many quirks from using Xoops.