Hi
I too have the same problem however this only happens (for me) on installations on my shared hosing package.

Running any current version on my local host and "Remember" works.

I wonder if this is not a cookie duration or dnn issue but to do with how or where DNN is deployed and/or users firewall and browser security settings.

This is a recurring thread so maybe it would be useful for those needing an answer to supply a little more information ?

For Me
Works: Local Host, IIS 6, Dotnet2, SQL 2K5 Express,  IE6, IE6.5, IE7rc, Firefox
Fails: Shared Hosting, Dotnet2, SQL 2K5, All browsers.
Security: Kaspersky Internet Security. Level = Medium High

Actually I would quite like to know how to safely remove this feature which is often very undesirable for many applications.
Currently I exploit the "fault" saying its turned off as its a big security risk for any organisation.

regards