When your car turns off after 10 minutes it could be a driver seat sensor that shuts off the engine if the driver is not in the driver seat.
A car shutting off after 10 minutes could also be a start stop system on the vehicle that shuts the engine down when the car is stationary for the 10 minutes to save fuel and emissions.
You can temporarily disable the auto start-stop system by pressing a button in your car, which is marked with an "A" and a circular arrow.
To permanently disable it, you can use an aftermarket plug-in device, a trailer light tester, or modify your car's settings with a diagnostic tool, though the latter requires professional knowledge.
When your car turns off by itself while parked it could be a result of a start and stop system or your car may have a system in which requires the driver seat to be occupied to keep the engine running.
Some cars are equipped with a driver seat occupant sensor that detects an empty driver seat and shuts the engine off.
Some cars also have an automatic engine shut off to prevent carbon monoxide poisoning as well.
If it's not a result of these safety features then the car shutting off while parked could be a result of a failing fuel pump, vacuum leaks, dying battery, electrical problems, engine timing issues or even a plugged catalytic converter.
A severely clogged or blocked catalytic converter can restrict the exhaust flow and cause your engine to shut off when parked.
And dirt buildup in your vehicle engines throttle body or a stuck idle control valve can also restrict airflow to the engine and cause the engine to stall.
Leaks in the vacuum system can also result in an incorrect air fuel mixture and cause the cars engine to stall.
Also issues like a weak fuel pump, dirty fuel injectors, faulty fuel injects or clogged fuel filter can restrict fuel flow and cause the engine to stall when parked..
And a weak battery or a bad alternator can fail to provide enough power to the engine and battery and cause the engine to die out.
And many modern cars have a start-stop system in them that is designed to automatically shut off the engine when the vehicle is parked and at rest to save on fuel and reduce emissions.