If this problem occurs for the mechanics and they cannot find the issue, you're taking the car to the wrong mechanics. Once you've got the proper tools, it's pretty much a process of elimination using logical reasoning. While the condition is occurring, we should be able to check the following and determine the nature of the problem:
- Is there fuel pressure?
- Do we have ECM function?
- Do we have spark?
- Do we have injector pulse?
- Do we have proper cam timing?
- Do we have compression?
- Will the fuel burn?
- Do we have any DTC's?
- Are all the fuel management sensors/actuators operating properly?
If I had the answer to your problem, I'd be happy to give it. The reason I can't is that there are too many possibilities and unknowns. Once some basic diagnosis is done and we know the system having the problem (fuel, ignition, etc.) is present, then we can narrow the scope to those things that could cause the sort of problem you have. Without that, the field is pretty wide open.