When you focus out of the Minecraft window/screen, if you leave for more than 5 or so seconds you will be disconnected a couple seconds later. 

This issue effects servers, peer to peer hosted servers and realms. There is no way to use another window to say reply to a message without being disconnected. 

How to reproduce:

1. Join an online server, friend's peer to peer server or a realm
2. Tab out or focus on another window briefly (10 seconds will do it)
3. Open Minecraft and it will show you are disconnected soon after.