I have noticed that if you just join and spectate, it doesn't boot you. I was in spectate for over 20 min. If you join a team and start playing, BOOT! Big red disconnected from the server appears.
I think that is a red herring though. I played some more last night and was able to get through an entire 45 minute session without a disconnect, only to have the very next game kick me within the first 5 minutes.
You will also get this disconnection dialogue simply sitting in the server browser, without a connection to a dedicated server.
Just FYI, I actually received a response from EA support, and am undertaking their requested debug and logging steps. I'll post more as I have it.
As mentioned above, the fact that it is not only Crysis (but also Crysis Wars, and Battlefield games) being affected
is actually a good thing.
EDIT
Some additional reading seems to point to one of the maser DNS servers at Gamespy being offline for unknown reasons (somebody forgot to plug it back in?). In any case, some of the Battlefield guys are saying that if you connect to a server directly via IP and don't use the server browser that the connection is improved. Have been unable to verify this myself, and your mileage may vary.