If the bulb is near the 150 watt limit or the whole assembly is in a fairly tight enclosure. The Socket Rocket maybe getting hot and the electronics in it maybe getting effected by the heat.
You were the first one to respond about my problem, Brian and it appears that you were right. I apologize for not checking further back then. Even though the problem lights are outside in the cold, open at the bottom and only 100 watts, when I checked tonight, the bulbs were quite hot. So hot in fact, I believe the heat was affecting the Socket Rockets. The only thing I can figure out is that the lights bulbs are hanging under the Socket Rockets and the heat was rising - and was trapped -- into the top of the light globe. It also may have something to do with the clear light bulbs that were in there too. I dunno but they sure were hot.
Anyway, I replaced all three bulbs with 26 watt CFLs because they are all I had on hand and because they would likely run cooler.
After several hours of testing with the new bulbs, the lights turned on and off every single time without fail or hesitation. It's probably risky to say it's solved but I have a good feeling about this fix.
Thanks again to you Brian and to everyone who shared ideas.