The "remember me" option in asp.net 2.0 will remember the user for as long as the Timeout period set in the forms authentication in the web.config
It’s really weird how it works as it is now. Below is an excerpt from a post found on the DotNukeForum:
How forms authentication cookies worked under asp.net 1.1
session cookies expiration = current datetime +the forms timeout value e.g. 60
persistent cookies expiration = current datetime + 50 years
How forms authentication cookies work under asp.net 2.0
session cookies expiration=current datetime +the forms timeout value e.g. 60
persistent cookies expiration= current datetime +the forms timeout value e.g. 60