Next time you lose connection, try doing through Terminal a ping to your cable provider's gateway (it should appear on your router's settings). If you get an answer, then the problem might be that some packets are getting lost in the way, thus making you seem "disconnected".
If the ping is answered, then try a traceroute to say, for example,
http://www.macrumors.com . There you might be actually able to see where the problem is occuring (by checking the last node to answer).
There's another probable cause: DNS trouble. If, when doing the traceroute
http://www.marcumors.com can't be resolved into an IP number, try doing a tracerotue (not ping, as macrumors doesn't anwser them
; or find another address to play with) directly to the ip number: 212.227.34.3 . If that works, you need to manually set your DNS on you router (or computer) to one that exists.
I've had all this problems happen to me at one point or another, and sometimes they would get fixed with resetting as is your case. It's probably a problem of packets lost between the cable modem and your provider, so I'd imagine ultimately they will just go and change it, and problem fixed.
Good luck!
EDIT: thought you said resetting the cable modem. Well, then its probably the router that must be replaced.