The modem is losing the cable signal lock. Either the incoming signal is losing strength before it gets to the modem, or the modem itself is destabilizing. The fact that it works for a few seconds after resetting it leads me to believe it could be the modem itself, but it could also be a weak signal.
Try this: Remove your existing coaxial cable. Go to the wall jack, and clean the outer threads with some bakeing soda slightly moistened with some vinegar. Make sure you do not get anything in the center hole, and wipe it down very well once you are finished. Next replace the coax cable with the thickest and shortest piece you can find that will reach where your modem needs to live.
Then, Switch your power plug for the modem to a different outlet, prefferably one with nothing else plugged into it. Fire everything back up and see if you notice any difference.
Comcast tech support should be able to run a Signal to Noise Ratio test from their server to your end without a tech onsite, so they should be able to see if there is an issue. They do have a website set up for techs to test things from your end back to comcast, but i can't find the URL anywhere from when they were last over here.