What is this DLink System your referring too? This the 655 router or something else?
I have the 6121 and just upgraded to a 6180 and have had the 655 online for days and days now.
Ensure the cable line going to the modem is in good condition. Sometimes ISP wont check there lines for quality. Demand it.
Ensure there isn't any T.V. line splitters on the cable line going into the modem. Having more will lower the signal the modem is getting thus causing disconnects. You can check he status of the 6121 modem by going to it's modem page at 192.168.100.1. It's commended if you need a line splitter, to only have one and a good quality one.
Swap cable between modem and router. Sometimes these in box cables are not make well. I recommend CAT6 and the shorter the better if possible. I use a 1 footer.
What Hardware version is your router? Look at sticker under router.
What Firmware version is currently loaded? Found on routers web page under status.
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.
Maybe someone can review your router settings with you using
teamviewer.