This problem has been plaguing me for a couple weeks. It happens on iOS and Windows 10 Beta (I don't have an android device). When my wife logs in on the same devices, no problem. Switch it back to me, bam it's broken again. I suspect my gamertag or character in Minecraft is corrupted somehow but there are no user-end tools to solve this problem.
I few e-mails w/ support have suggested resetting the realm. Resetting temporarily fixes the problem, but it always comes back within a day and I lose all my work!
I am having the same issue as Elliot Flanden above. One user is corrupted and kicks everyone off the realm. The user that's corrupted is the one that purchased the Realm. It happens on both iOS and Windows 10 Beta, and only with that account. If I sign in on my wife's account--no problem on either device.
I just changed my gamertag to see if that would fix it--and it did NOT. Logging in (same Microsoft account, new gamertag name) booted the other players (my daughter and wife) and wouldn't let me in. So it isn't tied to the gamertag name specifically. I will see if I can create a realm under my wife's account if it will have the same problem with me later on tonight.