On my Bigfoot I keep the fridge on Propane all the time including driving. Most of our driving is in hot weather and for several hours a day. There is no way the fridge will keep up under those conditions so keeping it on is a must. It rarely if ever blows out while traveling.
I did one trip to Las Vegas for a convention in July. I added some fans in the vent chase on the back of the fridge hoping to help the airflow in the extreme heat. Ironically, these fans even when not running changed the airflow dynamics of the that vent chase. The fridge would no longer stay running while driving down the freeway. It took a few trips with barely cold food before I admitted defeat on my "upgrade" and removed the fans. Since then, fridge has been rock solid. Lesson learned, the airflow dynamics can be something very difficult to account for but is a huge factor in wether the fridge will run while driving.
I know the newer compressor fridges are all the rage. Maybe someday when I have one I will think the same. In my opinion though, these propane fridges are really very solid. You just have to understand their limits and work within them. Turn them on a day before your trip, minimize opening the door (chase the kids out!), Keep a large block of ice in the freezer to help provide thermal mass and regulate temps. Expect that on a grocery run food is going to warm up the fridge for a few hours as the system works to cool it all back down.
The tradeoffs to these limits is a very efficient method to keep food cold that is simple and generally just works when it's used properly.