Yesterday I did what @unknown wrote in his comment above and it worked, I didn't have problems for ~2hr and the progress was saved. Today the saved game is still on the relams. But this is a workaround not a fix from the devs.
We have the same problems, after ~15 minutes we are kicked out the realm and no progress is saved. It's the 3rd day now, it's very annoying, please fix it.
As previous comment said, what's the point of paying when the quality of realms is so poor 😞
We are playing on win10 and Xbox One
I found a provider that lets you make your own bedrock server and it' cheaper than official but unfortunately xbox one players can't join custom servers, nice move Mojang :/