I advocate a magnetic key case attached to the vehicle somewhere (duct taped shut), in previous vehicles I've used bail wire to tie one to a spot underneath.
Be careful where you place the magnetic key cases. Anywhere near a wheel well and the first puddle you hit it will be gone.
I want to make sure your warning doesn't distract from my recommendation Ray, b/c you're making a very specific consideration. If someone places that magnetic case correctly on the frame, meaning full contact, it will not come off. My POV is a very off road capable Jeep Wrangler and after 100's of off road miles it has not so much as shifted position.
I've used the same case for ten years on 3 vehicles. Current POV, Dodge Charger, Ford F150. Put it on a flat area at any angle with full contact, it will stick. Putting it on a rounded surface would be foolish.