Vehicle stalls on highway suddenly, but will restart once we pullover and turn key again

After driving for several hours, our tahoe stalls on the highway. It will stall with AC on, without AC on. It will stall with cruise on and without cruise on. It will also stall up a hill and down a hill (or scary mountain pass such as it was). We typically have brakes for a few seconds, so pull over quickly, then put it in park, and start it up again. We don't seem to have any issues with it restarting. We take off down the highway again and it will be good for anywhere from 20 minutes to an hour. The last time it stalled was just as we pulled into town from the interstate. Any ideas would be wonderful, we have 2 mountain passes to navigate today and are hoping to find someone who can offer an idea to look into before we have to leave. No one wants to even look because they say it will check out on the diagnostic and will only give a code once it fails. I can't believe no one can even come up with an idea without the computer telling them what to fix!