Make sure you remember to check the "remember me" box when logging in. If you have been doing this, then please try the following, in order:
Clear browser cache and cookies
Restart computer
Make sure javascript is enabled
If, after that, you are still being logged out and you are on a Windows computer, please make sure you have up to date anti-virus and anti-malware software running, and run a complete system scan, repairing all issues.
If that still doesn't work, or if you are not on a Windows computer, please provide the following information: