There are two different timeouts.
The timeout for the general authentication page (iChain) that login.drew.edu provides has a one-hour timeout. If you're hitting Drew-based web services at any point during that hour, it shouldn't time out. That shouldn't, as far as I know, be causing you to be knocked off outside web sites. Essentially, that wireless authentication page does is add a rule to a Linux firewall that permits your computer to get to the internet.
Is this a new behavior, or have you seen this before?
Also, if you use the 802.1x SSID (Drew1x), that doesn't go through the captive portal and doesn't have a timeout because you have to authenticate to use it at all.