You might want to petition this as any toons left behind won't be able to return that apprentice to owner, either. (If they could, the apprentice would be deleted since you changed servers.)
I had the same problem a few years ago. I petitioned it and they gave me a nice new apprentice. However, it lost its titles, but since that doesn't mean much I was okay with it
Apprentices lose their titles if you pick them up. That information isn't persistent with your character, but part of the info stored in your house. When you pick it up, the info is deleted and the apprentice starts over even if you place the same one down again.
I did that during the last server merge and forgot to pick up one of my apprentices. If you /petition your problem they have been really good about helping to fix the issue with this one rather quickly.
Mine haven't lost their titles either. Have picked up/zoned multiple times. Switched houses a few times consolidating/switching crafting homes. No titles lost (to be clear, this is in the past two months)
That's been my experience as well. I didn't even lose my place in the recipe the apprentice was researching. Just picked it up, stuffed it in the new house and things went on as if it'd never been moved.
Mine have lost their titles when I switched to a different tradeskill apprentice, (coldain to othmir, for example) but not when being picked up.