Hello, I hope the following is of assistance.
There are a couple of common concerns that can give the fault you're describing.
The fuel pressure been incorrect, when you drive up a hill or accelerate hard the fuel pressure required is very high, if for some reason the pressure can't be achieved and is significantly different to the engine management desired pressure then to prevent possible engine damage the engine management will shut off the fuel to the injectors.
If the fuel filter hasn't been replaced recently then it would be a good idea to replace this as in around 75% of fuel pressure faults the filter is the problem. To confirm if this is a fuel pressure fault you need to have the engine management control module check for stored fault codes, the usual fuel pressure codes for this engine are P1211 and P0251. If after the filter is replaced these codes are still evident then the fuel pressure needs checking while measuring the amount of fuel returned from the injectors, this will help in pinpointing if it is an injector or the pump causing problems.
The engine will restart straight away as when you start the engine again the fuel pressure will be correct until there is a large demand again.
Another common fault is with the camshaft position sensor, if the signal from this is lost the engine management can't inject fuel at the correct time so again it will shut of fuel to the injectors to prevent engine damage. If the sensor body is black then it needs replacing with a revised grey bodied sensor, the usual code stored for this is P0340.
Start with these points, let me know if I can assist further or if you have more questions regarding this and I'll reply as soon as I'm able to.