The most likely reason is that you got banned for regen hacks. The way regen hacks work is that they speed up your in-game ticks. Normally I believe there are 8 ticks in one second, now your health regens ever 16 ticks or so. As regen hacks speed up your in-game ticks you'll heal way faster then normal ( side effect is that your hunger also goes down really quick ).
XAC detects regen hacks by the amount of traffic they receive from your minecraft client, when you use regen hacks you are sending a lot of packages to the server.
Now, here is the problem, when you are extreemly laggy your packages won't be send equally, sometimes a lot at once, this results in XAC thinking you are using regen hacks, thus kicking you from the game. This doesn't happen often, but sadly enough the system is not perfect.