If the engine has been cranking over ok, then the problem is not with the starting,charging system. If the engine cranked over slowly and would not fire until you jumped it, then you have a charging system problem. The reason for this is as follows: The ignition requires 12 volts to operate the computer and fire the ignition. The starter can turn with as little as 9 volts. You could crank the engine but it wouldn't fire.
The starting ignition control module is linked to the starting system by a red/light blue wire. It could be that something is causeing resistance in this wiring system or that the connections is/are heat sensitive. ( When you shut the engine off you stop the circulation of coolant and air through the radiator. The engine compartment and the engine itself heat up more than when running. This could be why the problem occurs after you shut it down.The extra voltage given while jumping could be enough to make things work again.
Also, there are a number of electronic sensors that will be succeptible to this higher heat and will shut down when too hot. These include: Mass Air Flow Sensor, Crankshaft Position Sensor, Ignition Control Module and Intake Air Temperature Sensor. All of these would allow the engine to fire back up after it cooled down for a little bit. Enough time may have elapsed to allow them to cool down before you tried a restart.
Let me know what develops.