Internet down on a Peer 2 Peer network

using verizon dsl with a Linksys Router (built in firewall) I find that in the mornings and varies times during the day my 30 user peer to peer network looses internet, but sustains local resources including access to the router. The users are not using too much bandwidth besides viewing webpages, and the local network seems stable. Any insight would be greatly appreciated.

PS. if you know where I can get a trouble shooting guide for peer 2 peer networks I would be very grateful