Venture ignition failure

I'm having a problem: the power supply to the ignition module keeps cutting out. After checking the crankshaft sensor and getting signal readings between 0.3 and 1.0 volts, I checked the ignition module's power supply. After several tests, I got 12 volts input, and that's when the engine starts. It runs for a while at low speeds, but when I try to accelerate, it stalls. I checked the power supply again, and it's dead.
I checked the fuses, and they're fine.
My question is, why is the power supply cutting out?

I'm hoping for some advice. It's a 3.4L GM engine. Thanks.