It just turns off completely

So are you assuming the charging system is quitting? What are the symptoms when the engine stalls? Will it still crank but not run? Will it restart if you let it cool down for a few hours? Do the head lights get dim? Must it be jump-started, and will it start then? Have you tested the charging system? Do various warning lights on the dash begin to flicker on and off before the engine stalls?

The generator, (alternator), IS the main part of the charging system. It provides the current to run the vehicle and it recharges the battery after starting the engine.

What you need to do is have the system tested, ... Or you can do it yourself with an inexpensive digital voltmeter. It sounds like it isn't working. First measure the battery voltage with the engine off. I can walk you through setting up and using the meter if necessary. The voltage will be 12.6 volts if the battery is good and fully charged. It will be closer to 12.0 volts if it's good but discharged. If you find it closer to 11.0 volts or less, the battery has a shorted cell and must be replaced.

Next, measure the battery voltage again with the engine running. It must be between 13.75 and 14.75 volts. If it's low, you'll need to measure the voltages on the wires on the generator. Those will help determine the next step in solving the problem.

You can find a perfectly fine digital voltmeter, (VOM), for around six bucks on sale at Harbor Freight Tools if you have one of those stores nearby. Walmart, Radio Shack, Sears, and any auto parts stores and hardware stores sell them too but there are many with features you don't need along with the much higher cost.