After accepting the mission, my ram suddenly disappears from under me. I have to abandon and accept the mission several times.
do you have any add ons running?
Are you running through the eating contest section? That dismounted me once.
Make sure you go wide around it
I think I figured it out. I had the Brown Ram in one of my action bars and apparently the mission gets confused about the ram mounts. When I deleted the Brown Ram from my action bar, the Barleybrew ram stayed with me.