I have a couple ideas. I think, not sure, but I think that if you are still using the coax connection, the menu options are not in effect, i.e. you are not outputting 720p via coax. You may be better off going back to the HDMI and experimenting with the output settings 1080i, 480p etc. and letting your TV handle some of the scaling.
The problem may very well lie with a poor signal and not with the 6416 at all. That's why I suggest going into the configuration page and checking your signal strength and gain.
Finally, I have had no signal loss or interruption on my current satellite setup with all the snow and rain we've had this winter. It may prove to be a valuable option if the cable provider is sending a poor signal that cannot be fixed.