I have experienced this as well. All players will be kicked from the Realm simultaneously and cannot rejoin for a short but random time. Like James it seems to be 2 -5 minutes. We are only a 2 person realm but this is for my 6 year old and I to spend time in something fun for him when I travel. But in the past day we cannot stay in the realm. I was able to export the world, but the export lost about 2 hours of game play. And I did find when I enter the realm if I do not move, then I am not kicked out. But If I move my character when looking at the map, I am thrown from the game. The map is an indicator map which has been expanded twice.
I am on Windows 10, anniversary update and the other is the latest version of IOS on an iPhone 5s. We are both on 1.0.0. The problem did not start until after 1.0.0. We had started playing on the Realm when we were both on 0.0.X. We do load updates as they come. I did export the realm and replace it with the backup and the issue stopped for ~24 hours but began again last night at 9pm. Thank you for your reply.