I suddenly started experiencing this issue since a day or three ago on BF5.
Every time I launch the game and join a server, it will kick me out after a minute or so and then allow me to reconnect to the EA servers immediately. When I rejoin the server, I'll be kicked out a second time. After rejoining once more, I'm usually fine. Until I restart the game.
At first I figured it must be something to do with my network, even though nothing had changed. Tried WiFi instead of ethernet and eventually cellular, neither helped.
I've been playing this game a couple of times per week since March without any trouble before this issue popped up.