Soulcatcher: I run cable modem through a router and have found that I have to reset both from time to time (turn on and off).
SC... I have my desk unit and 4 remote laptops run through the same system you do... (Cable modem / Router)... and find that a weekly reset is necessary to keep the 'glitches' at bay. Part of the routine now... Clean, scan, reset once a week.
(Caches, Flash and browser, when needed or once a week, whichever comes first.)