Shortly after my last posting (the one on the 20th of July), I decided just to try and move the power cords around to see if that would help (but still keeping the wires that goes from my device to the actual garage door opener disconnected). The existing setup was as follows:
I have an electrical outlet on the ceiling of my garage. I have a power strip/surge protector plugged into one of the 2 'plugs' of that outlet. I have my actual garage door opener plugged into that power strip/surge protector, and my 'device' plugged into the same power strip.
My change that I made on the 20th:
What I did was unplug the actual garage door opener from the power strip/surge protector and plug it into the 2nd 'plug' of the outlet on the ceiling (so no longer on the power strip/surge protector), leaving my device plugged into the power strip/surge protector all by itself.
5 days later (yesterday), I started experiencing the same problem as I described in my very first posting of this thread, so my change did not seem to help. 
I guess my next test would be to move my device physically further away from the actual garage door opener as hinted at by SurferTim...I will do this this evening.