I had this issue with the child account on the Fire tablets and recently switched to an Onn Android tablets for the larger app store. I'm seeing the same issue with child accounts there as well. I'll add the server to both my child's tablets. They can connect and play, but on re-opening Minecraft, the server list is reset and my local server is gone. This doesn't happen on my personal account (non-child).

Similar issue: 

1. MCPE-37685

Repro steps:

1. Create a child account on Xbox Live and Google Family Link
2. On the child account sign into Minecraft and add a custom server to the server list (save).
3. Server is listed
4. Exit the game
5. Re-launch Minecraft and go to the server tab
6. Custom server is gone.