"Corporal" was an Arabian, and I did NOT use a standing or running martingale on him. (1982-2009, RIP) IDK about how many people use a martingale when riding endurance, but I don't want ANY extra hanging equipment on my horse when I ride really rough up and down and/or steep trails. I've had horses long enough to have them step through the reins while stopped and grazing, and the same thing can happen if you give them their head and now have 4 pieces of leather working to catch a foot. You get a leg in the martingale and your horse's head will follow.
I've ridden many steep and mountainous trails, including the "goat trail" you take up to Harney's Peak, SD.
Really, guys, it's a little like barrel racers who can only think of racing and not listening. IMHO, get your horses under control before your endurance ride and drop the martingales.