Why does my router/modem dump my network after a while?

This is my 3rd router in a month and I don't believe its the router.  I build my network and everything is ok. Works fine when it's running. SEEMS like if I turn off the main computer or maybe one of the computers in the network, the network goes down.  I can still see the name of my network in all of the computers and it says it's connected with a good signal.  the Router shows, blinks like a good signal. Unplug does nothing.  Refresh from Comcast does nothing. If I reset the router, start over and give it a new network name, I'm ok until the next time it happens. If I go directly from the modem to a computer, hard wire. it won't work.  Shows  D-link...ask if I want to set up a network, then doesn't work.  It will work hardwired after I reset the modem.  I want say, as long as the 5 computers on the network are on, it will work.  

Can you help me?
Thanks
Art