Update: The pump quit again on 2-27-15 (4 months later), so I called the new pump man. At first he recommended replacing the black poly pipe with threaded PVC pipe. But when we pulled the pump, he noticed that the wire was just standard solid wire, and that it was not taped as well as he thought it should be. And when I told him that the original pump had worked fine without incident for some twenty years, he said he would not be opposed to giving the poly pipe one more try using proper stranded well wire and taping it more tightly. He said he was comfortable with either approach. Since going to PVC pipe would be a fairly substantial cost and would restrict me to having to use someone with specialized equipment like he has in the future, I decided to give the poly pipe one more try. Five months later, so far so good. If it fails again, then I will switch to schedule 80 PVC.
I really like the new pump man. Although he had an opinion when he first came, he looked at the situation and the history, and them modified his recommendation. He said that if it were his well, he would switch to PVC pipe, but then he has the equipment to replace it easily. He said that if he were in my situation, he very well might decide to give the poly pipe another try.