99 chevy suburban starter keeps going out

Sounds like gear cogs may have have broken of flywheel. Either that or the bendix is not pushing out to engage flywheel. Former is expensive. Latter not so much.

My problem is that the replacement starter will run outside the Suburban (hot wired) bendix kicks out, everything runs well...once I install the unit into the Suburban, it will not function..

I chased a starter issue on my 1998 C1500 PICKUP EXT CAB same vortec engne. Symptoms arent the same same but it ended up being the battery's negative terminal to engine block ground Wire. It was caked with grease grime and oil. Your Issuse could be electrical. Look carefully at the wires (-&+) and replace if necessary

there are two different starters for the 5.7l if you bought the wrong one it will eat up the flywheel . autozone only listed one starter and it destroyed my flywheel after calling a mom and pop parts place they asked for vin number and found it needed the gear reduction starter and not the one autozone sold me. it cost 850 bucks to replace flywheel and the new starter at a shop and i made autozone pay for the job, autozone doesn't have both listings in their computer while old time mom and pop shop did