This is one of the most frustrating problems that a broadband user faces. The ISP will probably blame the router. The router vendor will probably blame the ISP. The solution usually lies somewhere in between, but no one seems to want to help.
Random disconnect problems are generally hard to pin down because there are so many variables to consider in both your ISP's network and the router you use. The main way to attack the problem is with good old disciplined troubleshooting techniques and lots of patience. We don't have a sure-fire fix for you, but these troubleshooting tips should help:As much as it's a pain, get the router out of the loop and see if you have the problem with just one computer attached directly to the Cable or DSL modem. If you still have the problem, at least you'll only get the run-around from your ISP! If the problem goes away without the router, reconnect the router and upgrade your firmware to the latest revision. This is usually available from the router manufacturer's support website. While you have a normal connection, log into the router admin pages, and take a screen shot of the Status page, or at least write down the WAN IP, Gateway, and Primary and Secondary DNS information. Save this in a handy place next to the router. If your connection is being dropped multiple times per day, it may be that your ISP is forcing you off because they don't like routers connected to their network. Try using the MAC address cloning feature of your router and change the WAN MAC address to be the same as the one on the computer that was connected before you added the router. Next time your connection drops, first look at your cable modem or DSL router's status lights and make sure they are indicating normal operation. Next, before you unplug or reboot the router, log into the admin pages and check the Status page again. If the IP address is missing, you've somehow lost your DHCP lease. If your router allows you to do a DHCP Release and Renew (buttons are usually somewhere on the Status page if you have the function), try that. If the IP address information comes back, then you shouldn't have to reboot the router, but you may need to reboot or do a DHCP Release/Renew on your LAN's computers to get them working again. If your router has a keep-alive or auto-reconnect function (especially for DSL connections) try enabling it. Try to note if there's any pattern to the disconnection. Weather, time of day, power interruptions, running a particular application, etc. Keep a written log so that you have data. Speaking of power interruptions, try plugging the router and cable/DSL modem into at least a good surge protection strip, but preferably a UPS (Uninterruptable Power Supply). Prices for decent UPS' have dropped so much that it's not worth messing around with anything less if you even suspect power glitches or problems. Finally, do some research, to see if others have a similar problem. The Hardware forums on dslreports are a pretty good place to see if you have company in your misery.