The air conditioning has developed a habit of stopping working

Hello,

This could be due to freezing A/C lines after the A/C stays on for a little while.
Typically, A/C lines can freeze due to having moisture in the system. As the water will freeze with the compressor on and prevent he refrigerant from flowing and that stops the A/C from working. As you shut down the vehicle it thaws out and works again for a little while, until it freezes again.

It is possible to have a leak that allowed the moisture to enter the system. Moisture can also enter if any of the components was changed, which allowed moisture in.

One way you can check for leak in the A/C system is by adding dye to the refrigerant. As the system cycles the dye will leak out (if there is a leak), which is easier to find.

Here is a helpful video of how to find A/C system leaks:

https://youtu.be/yrhWKlQEPWw

Please let me know of any questions.
Thank you.