There are 2 places in the web.config file I have changed to stay logged in for 10 days (changing the values can increase or decrease the amount of time). They are locataed:

somewhere around line 39(in my web.config):

<add key="PersistentCookieTimeout" value="14400" />
    <!--use as persistent cookie expiration. Value is in minutes, and only active if a non-zero figure-->

and again about line 109:

<!-- Forms or Windows authentication -->
    <authentication mode="Forms">
      <forms name=".DOTNETNUKE" protection="All" timeout="14400" cookieless="UseCookies" />
    </authentication>

I haven't had a problem with staying logged in since.

Good luck,

Mike