I too am I having the exact same issue as the OP. My ISP is Cox Communications in Florida. I've yet to ask them to check our lines, but a check about a year ago showed that they were fine.
I've had this router, DIR-655 | Hardware Version: B1 | Firmware: 2.00NA, for about 6 months now. The problem has only showed itself for about 2 months - which I find very strange.
Anyways, I tried changing the settings recommended here:
Ensure DNS IP addresses are being filled in under Setup/Internet/Manual?
Turn off QoS options.
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.
Ensure devices are set to auto obtain an IP address.
Set Firewall settings to Endpoint Independent for TCP and UDP.
All devices on my network are connected wireless. This includes various makes and OS of PC, a mac, a printer (Brother), and occasionally a Droid phone and iPod Touch.
I'm really running out of options here. The internet connection through the modem (Motorola) is fine. I ran a test of it overnight by auto refreshing various webpages.
One note I will also add is that you don't necessarily have to be using Skype, AIM, MSN, etc. for this problem to occur. Just casual web browsing effects it.
I've witnessed the problem when I'm the only person on the network. I've witnessed other people on my network encounter the problem regardless of who's computer is on at the time. The only device that is always on is the printer - I'm tempted to remove it from the network for a day to see if that resolves the problem.
On a side note: The time never stays correct on the router. I've synced it to my computer time and tried an NTP server... I don't know if this could be a problem but it makes the logs hard to follow.
Note: I am a total router newbie. Please be nice and explain what to change thoroughly to me. All help is appreciated!
Thanks in advance.