I have that exact same router and figured out it was getting nailed by a computer infected with spyware!
I was going nuts until I looked into the device's log... saw hundreds of
Jan 30 02:39:47 UDHCPD sending OFFER of 192.168.0.102 Jan 30 02:39:47 UDHCPD sendOffer : client is in lease/offered tab
le Jan 30 02:39:47 UDHCPD sendOffer : device_lan_ip=192.168.0.1 , de
Don't exactly recall what I did to fix it, cleaned each computer, changed the wifi key and presto!
You could also try installing ddrwt or tomato ( I don't recall which one isnt compatible) that have better "defense" mechanisms. What I found in some forum, after intense googling, that the router had "fuse plug" to prevent it from getting clogged up it would just soft restart itself to drop any connections... this with the latest firmware, was never fixed.
Product Page: DIR-601 Hardware Version: A1 Firmware Version : 1.01NA
Make sure you scan each computer, change wifi password AND type (I think it was wpa2 to wpa, something that windows 8 doesnt play friendly with that router and wpa2 ).
And look at the log or enable it.
Also, my router was running in Wifi G... not Wifi N... that has to be done manually, because the router, for "compatibility" issues, defaults to wifi g...
So again, retracing my steps, cleaned computers, changed wifi password AND mode, changed and made sure wifi N was default and not wifi g.
My final step was installing ddrwt or tomato, as I hate not being able to fix something... if that didn't work, I think I would have been in the same spot as you.