Websites like this one often make use of the ASP.NET Forms Authentication schema. That schema has an optional parameter that will allow you to admin how long the 'Keep Me Logged In' functionality will remember the person. It does this using a cookie and setting the cookie timeout.
So, here is the snippet of code that you need to administer this and change it from it's default 48 hour setting
You'll find this code on the ASP.NET menu