This is obviously an ongoing issue that has more than one cause, as my friends often experience this while trying to connect to my server. It started sometime in the mid-2014 1.8 snapshots. Also, something I find interesting is it allows them in for a little while, but they can't break/place blocks, type messages, or do any action besides take damage it seems, and then it kicks them off after 30 seconds – 2 minutes. I've also been kicked off as well.
I'll look into that possibility! Is it possible it's caused by allocation of too much RAM?