Let me see if I understand this. You have a DIR-600L and the wireless will stop working, but wired connections to the router will keep working?
If so, when it happens, can the wireless devices still "see" the network name when you scan networks around you? If you can see it, can you connect just not get online? Any error messages?
Also, what do you have the DIR-600L connected to for ISP? Modem? Gateway? What model? Just making sure you don't have it connected to a wireless gateway and THAT wireless is interfering with the wireless of the DIR-600L.