Tony P says:

Hi Doug, Some of this may sound like common sense but here goes, did you connect lights in series of parallel. If you hook them up in series, one light to the next, you have 12v x 20 = 240v draw or 2v x 12 = 24v draw, either way the voltage maybe too much and over heats and shuts down the power. In a parallel circuit you hook up each light to a buss or main line that feeds each light indivdually, this way no matter how many lights you put on it, it should work. If you dont understand series and parallel, get a basic wireing book and it should help you with a lot more than just this. I always have one handy to hopefully minimize mistakes.
Or it could be as simple as a kinked wire ready to break at the power source or some where in between before it gets to the lights, when it heats up it separates just enough to loose power and when it cools off it reattaches itself until one day it will just break away clean, dont forget you are using very tiny wires and we may not even feel the heat. Tony P