The Specs of the Power Supply I Used
Does the charger have a max amperage rating? I get the minimum but I'd be more interested in the maximum. Usually it is listed.
How long does it run before shutting down? You might monitor the amperage as it is running. It might heat up and need more current.
Is it powering anything else on any of the rails? If you do the math on the power ratings, it adds up to more than the max of the supply and you do have to take that into account.
You can also look in the power supply as it cuts and see if a component is heating up(like a bad cap). FLIR is good but if you have a laser IR sensor, that will work and is much cheaper and handy to have around the house.
Confirm you are using the 12V A line and that it is not tied into the B line at all(combined).
Make sure you have 5v linked to the sense line. Does it have a resistor here(and properly rated)?
You might try powering something that is less load intensive and see if you have the same problem on the 12V rail. It might keep you from chasing a red herring.
Sometimes switching power supplies have reverse polarity protection and some loads(particularly higher loads) can cause it to trip. Sudden current spikes are sometimes the culprit.