Seeing as how I just went through this, ill advise what mine was.

My symptoms were the pump would stay ON, unless unplugged. It burnt out one and I had to get another one sadly. My problem was the air pump relay armature was stuck and had burned some.

I had to buy some emery paper (got a few sheets from autozone) and some contact spray(radio shack) to fix my issue. I took the armature out and sanded it with the emery paper and sanded the relay all the burnt areas then I cleaned it up with contact spray and so far it has been fine.

Now your car might not being doing what mine was but ive laid out a possible problem and solution for you.