Running the latest version of DotNetNuke, version 5.6.1 and cannot find a good answer to why Username and Password cannot be remembered on a DotNetNuke site. This thread goes on about cookies but really misses the point. User 'ptleitch' puts it best when he askes:
"Well thats all fine and dandy. You learn something new everyday. The problem is, my users are submitting issues along the lines of they expect the "remember login" feature to auto-populate the "username" field in the login control, and I've got nothing to tell them other than they're out of luck."
First, to enable the functionality, as orka said, you'll want to set the PersistentCookieTimeout in the web.config to something greater than 0 (value is in minutes).
In addition to that though, I'd suggest altering the verbiage presented to the user on the login screen to be more accurate. "Remember Login" does make it seem like it's just going to auto-populate your credentials - which, functionality-wise, doesn't really make sense.
So, I'd recommend changing "Remember Login" to "Stay signed in."
You access (and update) the verbiage through the DNN user interface by browsing to Admin -> Languages -> (edit English static resources for site link) -> Local Resources -> DesktopModules -> Admin -> Authentication -> App_LocalResources -> Login.ascx.
On a little bit of a tangent - I'd go as far as to suggest that you should change everything from "Login" to "Sign in" as well (e.g. User Sign In, Stay signed in, etc) - just because it makes more sense.