Internet help for Verizon! Please

Okay, I have a Verizon modem model 6100G. Also a NETGEAR router. The only things I have connected to the Internet are my Xbox, IPhone, and IPod and occasional Hp home Computer. (Which is not the routers fault it keeps disconnecting) Every so often lately (been going on for about 5-6 months now) My Internet will stop working, my modem has three lights for Internet, data, and DSL, and the Data and DSL with keep flashing fast. The Internet light will sometimes turn red but that's 3/10 times. It will have really good times like no issues for a week. But this past 2-3 weeks its been working for about 10-30 minutes and will just stop working. We have Verizon phone too, but that works fine, at the moment. FiOS is not available in my area. To get it working again for a little bit I will unplug the Modem and turn off the router, and it will work for a bit, not work at all, or for about 10-30 minutes. Any suggestions to help fix it, or should I just switch to a different company instead? (Trying to save some money) All answers are welcome please and thank you!

Switch to anther internet service provider. Virgin media, BT, SKy in that order. You will get a free router with there packages