Thought I should update my story a bit.
We got home from our Christmas vacation, I covered the trailer and left it till just last week. Imagine my surprise, seeing all that Eternabond that had lifted six months earlier, now under the July sun and under the cover had stuck itself to the rubber roof and everything else it touched. I caulked the leading edges and we went camping. Not far but it did rain and we stayed dry. The damage is done however. I pulled the ceiling and insulation in the bathroom off and am letting it dry for the rest of the summer. I'm really not in a roof replacing mood.