Sometimes they make it through a loading screen, most of the times they don't. What gives? I was pretty excited to finally get it and it seems pretty useless if I can only keep them in the current cell.

They are buggy. This happens sometimes. You just need to go back through the door. They will usually be there, most of the time they are dead but you can just reanimate them again. Fast traveling into a city actually spawns them at the stables. Sometimes they will spawn with you but not always. Best to save before going through a cell or fast travel.

WHOAH THANKS. Did not KNOW that. I'll check the stables at a city next time. I've only had trouble with my thrall a couple of times, one was exiting a cave, she just WOULD NOT
exit it. I even tried a trick that is suggested if an npc is stuck trying to exit a cave, for a quest ( that shout that blows stuff out of the way), she'd still not zone.

I love her because she is a Thalmor soldier, who should be around level 36 (max, for that area I think (Thalmor embassy.) I off'd her at home, smithed her armor up to
legendary and enchanted it. Then shoved it back in her corpse with legendary daedric sword, shield and bow. She REALLY goes to town on stuff. She puts my regular
folower, Mjoll, to shame. Its fun to have them both with me.

Most of the time, she keeps up with Mjoll and I. I've only had her die once, when she kind of just stood dumbly on a "swinging spikey door" trap, for way too long.
I really hate thalmors, so its fun to have one of them as a perm companion from their embassy (when I go back there to kill more.)

Also, if you fast travel to a cities stables (and not into the town!) the Thrall can get sent elsewere and if you watch the road you will
be able to see them running to you, well this is the case with larger Thralls (ie. Giants) dont know if Mamoths do this.

I found out where they went by Enthralling a quest giver. After the quest was complete, the first time, I was met on the road by a someone. They started the quest again. It listed in my quest log. This is just a bug, but the original quest giver was still alive and still at the same location. They would still have the floating quest marker on the map. I returned and killed them. Now I had a DT that was marked on my map. When they didn't spawn with me, I could pull up the map and see where they were.

I have also had this problem with cities
Also you lost your thrall was it in a cave with certain group of marauders wearing Leather by solitude that place is bugged where thralls cannot get out