Delete the cookie and try again. That usually solves things.
Problem is that cookies can become... I don't know... broken somehow. They're an outmoded method of storing information for sites that really needs to be depreciated in modern browsers.
Clearing your internet browser cache/temporary internet files is a good first step. If that doesn't work, try something for me: head to the Edit Options page in your User CP. Scroll down and find "Forum Skin". In the drop-down box, select "default vb380". Click "Save Changes" at the bottom once this is done. Your theme is now the default. Try logging in and using the "Remember me" box with this theme. See if it lets you stay in. If so, we have a theme problem. If not, the issue is on your end and we can try diagnosing further.