We were in the same boat. We were towing with our JLU Wrangler and using the cheapie strap mounted extensions and they were prone to flying off. We picked up an Armada to become our tow vehicle, and those cheapie mirrors worked even worse. So then I bucked up and bought these bar mirrors, and they work really well (for the one time we we've towed with the Armada so far).
Amazon.com: Dometic DM-2912 Milenco Grand Aero3 Towing Mirror (Twin Pack): Automotive
Amazon.com: Dometic DM-2912 Milenco Grand Aero3 Towing Mirror (Twin Pack): Automotive