When you said you disconnected it from the TV tuner and plugged it directly into the modem, do you mean you only had one Coax cable between the two of them? or is the cable coming off a splitter? If you have a splitter hooked up to the line that could be part of it, either that the signal is to weak to be split and still be functional, or the splitter is actually going bad. If you only have a single line then i'd suspect something with the modem to be honest. If you call in to comcast you should be able to get an HSI rep to look at your "SVP" and brink up your modem and check out the signal level to the modem and have them look up the "history plotlines" and they can check and see if the modem itself is indeed resetting or if it's a lack of signal that when it drops off causes you to lose connection.
if the person you talk to doesnt know what these things are, hangup and call back, you got someone who doesn't know how to do their job on the line and you don't want to waste your time as they stumble through what to do.