This has happened to me twice now. I'll break down what happened right before each time.

My friend is hosting a game at the Camp, and I join. We try to load into a mission together, and it kicks me back to the menu with the error "The connection to the host was lost." I press the reconnect button, then I finally make it into the mission, and the cutscene plays. Partway through the cutscene, it tells me I'm down. My friend's cutscene normally finishes first, and he is healing me when I finally get out of the cutscene.

His computer is much slower than mine, and when I host, things load quite a lot faster for me. My suspicion is that my computer gets all the assets loaded in first, tries to connect to his, but his isn't ready yet. But by the time I get kicked and reconnect, his is up and running and I join just fine. However, my character is present on the map for some reason, and has a chance to be killed by enemies while the cutscene plays.

EDIT: Seems to be unrelated to reconnecting.