Login doesn’t stick

Before upgrading to 2.0, I would allow WordPress 1.5 to remember my password, and I would be logged in until I cleared my cookies. Now with 2.0, I have to log in again after I leave the backend of my site. It can get quite annoying. I never click the “Sign out” link, and checking the “Remember me” box doesn’t help. I’ve deleted my cookies and tried again to no avail. What’s the problem?