2001 gmc yukon tow haul engaging disengaing on its on

You will need to take it to a parts store like NAPA and see if they will read the tcm (transmission control module) for codes, if all else fails then take it to a transmission shop and ask if they can scan it for codes and check the functionality of the tow haul button if it is not functioning, it could be just a broken wire from flexing at the base of the shifter.

You need to have a diagnostic scan tool hooked up ,glitch in one of the control modules or a wire in the circuit shorting to ground ! probably something simple but hard to find ! With a factory scan tool they can check the input signal to the BCM ,PCM .
Tow/Haul mode enables the operator to achieve enhanced shift performance when towing or hauling a load. When tow/haul mode is selected, the tow/haul switch input signal to the body control module (BCM) is momentarily toggled to zero volts. This signals the powertrain control module (PCM) or transmission control module (TCM) to extend the length of time between upshifts and increase transmission line pressure. Cycling the tow/haul switch again, or cycling the ignition switch disables tow/haul mode and returns the transmission to a normal shift pattern.

Yes, it probably is. It likely has a trailer towing mode that modifies the transmission shifting.

ckeck all fusses &relays

The wires are probably broken. They follow the shifter down into the steering column. After many years of shifting the wires break. You can find the wires inside the rubber piece that surrounds the gear shifter. They're orange. You can splice them and put them back in.

This is only an idea-pull column shifter boot-you will notice a ORANGE wrapped wire which runs from the button on the shifter down toward the steering column. This is the Tow/haul wire. The way this is positioned on the steering column will cause the wire to be pinched when ever the steering wheel is adjusted. This pinching can cause a short or cause the tow/haul not to work at all. NOTE: Inside this orange wire wrap are two very fine fiber wires. Be careful and good luck

The autoride is likely coupled with the tow/haul function. When towing, you want firmer suspension, tighter cornering, less sway, along with the firmer transmission shift and different shift points. This helps keep you from tipping the vehicle when you have a high load because the suspension swayed too far. The vehicle is supposed to be a luxury vehicle, so this changing characteristic allows it to ride smoother and softer when you don't need the trucklike suspension.

check fuses... if ok the wires going to that button like to break ... unscrew handle end and inspect...

It saves your transmission from costly repairs. The little bit of fuel you think you may save by not using it, will certainly not outweigh that big bill for new transmission. Saves transmission from shifting up & down too much.

most likely switch