Lost connections through cable can be confounding. I found that the cable itself (RG59 or RG6) can cause an issue when split too many times prior to the modem. I requested that my installer run one line directly off the main to insure a good signal.

You can eliminate the router as the problem source by taking it out of the mix and attach the modem directly to one PC. If the problem persists, then the router is ruled out leaving just the cable or the modem or the ISP. In any case I would make it their problem.