Battery does not stay charged!!!

If you take it to any parts house that can test ( I prefer NAPA) They can check it on the car and tell you if there is a bad diode or anything wrong with it. The can also bench test it if you take it off the car and carry it in. If you take the feild wires off the alt and put your test light to it with the ign. off and there is power on the terminals then there probably is a bad diode in the alt. And to answer your question about the relay. With the key off there should be no power on any terminal but the BAT terminal. If there is then it is possible that the relay or maybe even the key switch is bad. I would check that and then let us know what you found.