What ISP Service do you have? Cable or DSL?
What ISP Modem do you have? Stand Alone or built in router?
What ISP Modem make and model do you have?
If this modem has a built in router, it's best to bridge the modem. Having 2 routers on the same line can cause connection problems.
To tell if the modem is bridged or not, look at the routers web page, Status/Device Info/Wan Section, if there is a 192.168.0.# address in the WAN IP address field, then the modem is not bridged.
Some things to try:
Ensure DNS IP addresses are being filled in under Setup/Internet/Manual? You can find these under Status/Device Info/Wan section.
Turn off ALL QoS (DIR only) GameFuel (DGL only and if ON.) options. Advanced/QoS or Gamefuel.
Turn off Advanced DNS Services if you have this option under Setup/Internet/Manual.
Turn on DNS Relay under Setup/Networking.
Setup DHCP reserved IP addresses for all devices on the router. Setup/Networking
Ensure devices are set to auto obtain an IP address.
Set Firewall settings to Endpoint Independent for TCP and UDP under Advanced/Firewall.
Enable uPnP and Multi-cast Streaming under Advanced/Networking.
What wireless modes are you using?
Try single mode G or mixed G and N?
What security mode are you using? Preferred security is WPA-Personal. WPA2/Auto TPIK and AES.
What wireless devices do you have connected?
Any cordless house phones?
Any other WiFi routers in the area? Use
InSSIDer to find out.
Turn off Short GI and Extra Wireless Protection if you have it. Under Advanced/Advanced Wireless.
Enable uPnP and Multi-cast Streaming under Advanced/Networking.
I was having the same problem with my newly-installed DIR-615 router's wireless service: it would work fine for about a half a day, but then disappear (even the SSID was no longer visible), and an unplug-replug of the power to the DIR-615 got it back up and running.
Of course, that was not a good permanent solution, because that wouldn't be possible if I were not physically there in the room when the difficulty arose 
Here's something I found out that seems to be providing a permanent solution for me:
The instructions for the DIR-615 indicated that the "Channel Width" should be set to "Auto 20/40MHz" (available by going to: "Wireless Settings/Manual Wireless Network Setup"). Mine was set, instead, to "20MHz". Resetting that to "Auto 20/40MHz" and allowing the router to reset itself did the trick for me (at least, it has survived longer than ever before and has not yet lost the wireless service and the SSID has not disappeared...). The other settings on that page were OK as they were set by default for me: "Enable Auto Channel Scan" was checked; "Visibility Status" radio-button was selected.
Hope this helps someone else!!