Brian Moon has posted a tip (and a bit of code) he's worked up to help make a users cookies last a bit longer than they were originally designed to:

When you start a session, if the user had no cookie, they get a new session id and they get a cookie. You can configure that cookie to last for n seconds via php.ini or session_cookie_set_params(). But, and this is a HUGE but for me, that cookie will expire in n seconds no matter what.

His method provides a way to extend the life of the cookies currently set for the domain by changing the time to live through a series of ini_get calls wrapped in a setcookie() call.