You better check the transformer spec. If the transformer is rated at 150W and you'd installed 5 x 40W =200W, the transformer is overloaded. When the lights have been turned on for awhile, the transformer got too hot and the overload circuit cuts off power to the lights. It will stayed off until the transformer cools down, then the lights will come back on.

One thing you can try. Remove couple of lights or fixtures from the track and see if the lights will stay on

In speaking of transformers, are these low voltage tracks? We are electricians in Dallas and recently installed several tracks in a salon. These are hard wired and have no transformers. If you are in fact dealing with low voltage, you cannot overload the transformer.

Steve has indicated transformers, I am assuming he has bought a low voltage light tracks that has a 150W transformer and separately purchased 5 lights with 40W bulbs, that will overload the transformer.
Steve, have you try to remove couple of light fixtures yet?