This is what happened to me today
I went and stable my Cu at the luna stable. I took out my greater dragon. then I had to go afk so I restabled my greater dragon. I got on my ethereal went threw the gate to umbra logged off. I came back a few minutes later logged in and my CU was at the umbra gate with me. I never took it back out of the stable after I stabled it. first time I ever used the luna stable to I always use moonglow inn stables, and I was in the 2d client when it happened. I havent been able to get it to do it again.
Now Im thinking if I logged for the night got on the next day would my CU be gone like others have lost their faction horses or dread mare . One of my guildmates lost their dread mare stabling it taking out their greater dragon next day the dread mare was gone.