Password-protected posts are redirecting to wp-login.php

I run WP 2.9.2 on one site and 3.1.3 on my own, personal site. I have never been able to get password-protected posts to work correctly.

The site running 2.9.2 is for the orchestra that I play in, with posts that are supposed to be password-protected for musician-, management-, and board-use only. When the site went live, all p-p posts appeared correctly with their login fields, but when users logged-in, they were always redirected to wp-login.php — or, in some cases, the dashboard! I had to abandon the password-protection, and now those pages are visible to anyone if they know where to look.

I just tried a p-p post on my own site (3.1.3), and I get the same result. Any ideas? I thought maybe it was a plugin conflict, but the only plugin installed on my 3.1.3 site is Akismet.