If you have any splitters, replace them. Them are the most common cause of signal loss, and although the TV is unaffected you will find that the Internet is affected. Matter of fact, even if you replace the splitters (which you should), try disconnecting the cable where it comes into the building and connect directly to you computer with a short, patch cable. If you experience no problems them the problem is in your indoor WAN connections.
Similarly, loss of shielding or bad connections on your outdoor cable will cause the same issue - TV OK but Internet slow or intermittent.
Finally, your cable is not a dedicated connection to your ISP. Increased Internet activity in your neighborhood will impact your performance. In the early 2000s people were complaining that they were dripped down to dialup speed at certain times of day, not sure if this still applies or if it applies to you.
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