[MTBikerTim]

Grab the manuals for both the router and the modem and go through the setup properly on both setting up security etc how the manuals suggest. If you can give us the models of the router and modem we can give you a good detailed setup to follow. It shouldn't just drop out like that and it sounds as if something isn't right. Could be something like brian said that you have 2 dhcp servers running on the same network but it's unlikely.