Every horse and every situation is different. My similar experience, for what it’s worth:
In summer 2001 I moved, and had my then-horse transported, 350 miles. She had been regularly trailered to small open shows for the past several summers and had never been a difficult loader, but earlier that summer, she had started balking when asked to load. As with your mare, there was no obvious fear behavior (I’m not saying there was no fear, just no readily apparent sign of it in the horse’s demeanor) and no readily identifiable reason for the change in behavior (same trailer, environmental conditions, length of trip, workload at the show, etc. as always).
When the professional horse hauler showed up for the big move, the horse again balked. The hauler had a not-too-long, stiff-ish lariat rope (what online western stores sell as a “piggin’ string” or “youth lariat”). He wrapped it loosely around her barrel, closer to the hind legs than the front ones, and lifted it gently against her stomach as I asked her to step onto the trailer. She immediately and calmly stepped aboard as if nothing had ever been wrong.
I got my own “piggin’ string” after that, though I never had to use it again. I suspect the effect is somewhat similar to, but gentler than, the “butt rope” method (which you can find out all about by Googling).