1990 Acura Integra backing out of the parking space the engine quit/stalled

1990 Acura Integra 1.8L DOHC mileage: 111,000. The problem has happened twice. The first time I had pulled into a shopping mall and after about 15 minutes I started the car and as I was backing out of the parking space the engine quit/stalled. I tried starting it and it would not start. I came back the next day and the car started right up with no problem. I was able to drive it (my normal driving habits) for a little more than a week, when I was going about 45 mph the engine just quit on me again. After getting it towed, it started up again the next day. Both times, it stopped; I heard no unusual noise or felt anything out of the ordinary. I took it to a local service station and they couldn't find anything wrong with it, although they mentioned an ignition system problem with a newer model Integra. They looked at it, said it appeared to be fine, and were reluctant to replace it on a "maybe" that would cost about 500 dollars. I called an Acura dealership and the service department (I did not talk directly with a technician) suggested that the hot engine restart" problem might be due to a problem with a coolant (ECT) sensor. A man in the parts department mentioned that there had been a bulletin on an igniter problem with models around that year. Do any of these suggestions make sense?