It's certainly not supposed to do that. When it happens, and you type FN+F5, does it say the radio is off again, or does it say it's on and turning it on and off again make it start working?
Have you tried it on campus? If it doesn't happen on the Drew network, then it's a problem with your access point (a signal problem perhaps, or a configuration issue.) I've seen all sorts of issues with APs based on whether the network name (SSID) is broadcast, if encryption's on, etc. Sometimes the behavior varies from vendor to vendor. Also if the signal's borderline you might see similar behavior. The periodic nature is interesting, though it could actually indicate a periodic interference that's causing the connection to be broken. The fun thing about wireless is that unless you have an RF analyzer it's really hard to track stuff like that down.
It could be a software problem. Use the Lenovo Software Updater and get the latest versions of the Lenovo drivers, that may help.
Of course feel free to bring it by the Helpdesk to see if we can help you.