RESPONSE
Most likely cause of this issue would be the ignition control module. When an ignition module is failing it will act just like you described. It sounds like the shop you took it to is just throwing parts at it with the hopes it fixes it. You may want to take it to a different shop and start from scratch. They may want to diagnose the issue and run a few tests but better than paying for parts you do not need.
What you need the shop to do
You will want to have the shop test for what the engine is not getting when it will not restart. This will help guide them in the right direction. An engine needs four things to run and without one of them it will not run.
- Spark
- Fuel – Fuel Pressure and Fuel Injector Pulse(it sprays fuel)
- Compression
- Timing
We can rule out compression and timing as we know it does run for a short time. And since it starts up after it cools down it is less common for it to be a fuel related issue. The shop can test for fuel and spark when it is not starting. Since it happens often it shouldn’t be to difficult to test. Once they identify what it is not getting they can concentrate on the individual components of each system.