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:
Repro steps:
Create a child account on Xbox Live and Google Family Link
On the child account sign into Minecraft and add a custom server to the server list (save).
Server is listed
Exit the game
Re-launch Minecraft and go to the server tab
Custom server is gone.
Thank you for your report!
We're tracking this issue in MCPE-113636, so this ticket is being resolved and linked as a duplicate.
If you would like to add a vote and any extra information to the main ticket it would be appreciated.
Quick Links:
📓 Bug Tracker Guidelines – 💬 Community Support – 📧 Mojang Support
📓 Project Summary – ✍️ Feedback and Suggestions – 📖 Game Wiki