Ok, no relay that I can see on any diagrams I pulled from google. I'd pull the harness from the back of the HU, and measure the voltage at the light green/yellow wire, should be hot at all times. Next check the voltage at the yellow/black wire should be hot when key is on or in accessory. Check the voltages from those 2 wires to the negative battery terminal, and compare that to readings from those 2 wires to the black wire in the harness. If the readings there are the same (within a few mV) then you likely have a problem with the HU itself. If they're different, try running the same test at the factory harness where the after market harness connects. Bear in mind the after market harness may have different color wires than I mentioned, please reference the factory wires to find the corresponding wires on the after market harness. Also note that the diagram I pulled was for a 1997 k1500, you may want to check for a diagram for your vehicle if yours is from before the mid generation facelift.
My best guess from what I've heard so far would be a low voltage cutoff, you're probably getting enough voltage to keep it on, but something else running drops the voltage below the threshold; could be the A/C, lights, turn signals, or some random combination thereof. It could also be an unreliable connection that loses connection due to movement or vibration. Make sure to move the wires around during voltage readings to see if you can replicate the symptoms.
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