Is your router assigning an IP to the ATA? If it is, you might just give the ATA a static IP from the router? It also could very likely be a problem with the ATA itself.
I agree. It has to deal with your router dropping the IP address of the phone adatper. That's why when you reset everything it works again. Try assiging the ip address of the phone adapter you your router assuming you have a router with QOS. You can find the ip address of the phone by dailing **** and entering 110#.