I am not an expert, but I have found that Comcast boxes are VERY sensitive to power supply changes. Where I live we often have "blips" in power, and the Comcast cable box is the most sensitive, and will cut out completely. In fact, the cable box is the only electrical component to fully "go out", though only for one second or so. Of course the box then resets itself (where you lose the "guide", "info", etc.)
It may be that the outlet, power strip/center, etc. where you have the box plugged in to is "marginal" for current draw. Whenever a "draw" occurs in your house (refrig, lights, etc.) there is just enough current "drop" to your cable box to "shut it off", if even only for a microsecond. Technically, a Comcast cable box is never "off", it is in a Standby state.
Before you rerun any connections cables, is it possible to plug the box into a dedicated outlet? It is also possible that your signal strength is marginal at this outlet/box. I have had a chronic issue with "audio drop" from my Comcast box, and after several tech visits, one finally admitted it is a "signal drop" (like a packet loss) that might require rewiring the entire house and line from the trunk line.
I personally do not think this is an HDMI cable issue, rather a power supply issue to the box. However, perhaps the marginal power supply issue is highlighting a "next weak link" in an HDMI cable or run.
Sometimes I have to remind myself that I bought all this "stuff" to enjoy it!