It found out you were doing gift searches and none of them were for it. A jealous router is a dangerous one.
First, rule out other things as the issue. Does the disconnect happen on both wireless and wired connections?
Connect the computer directly to the modem and see if that is stable. Make sure you have a software firewall running though for safety. Try that way for a day or however long it usually takes to crash.
If it stays stable, plug the router back and do a firmware update, test again.
Usually the wireless part tends to fail before the wired (my router is doing that now, and so have a few others I checked on), if that is the case, you need a new router.