Engine will not stay running

Hello,

It sounds like you might have a bad alternator.
When the alternator fails it is unable to charge the battery and that leads to the engine shutdown.

One way to test the alternator is to check the output to the battery with the vehicle running. But since the vehicle stalls as soon as the cable is removed, the best option would be to remove the alternator and have it bench tested.
Most auto parts stores have bench tester that you can have them test for you.

https://www.2carpros.com/articles/how-to-replace-an-alternator

I have attached diagrams for your reference.

Please let me know if you have any questions.
Thank you.

If it is a bad alternator, those alternators run anywhere from $100.00 to $150.00.
If you, do it yourself then that's all it could cost. If you have a shop, do it then it will depend on their labor rate.
Let me know how it goes.