I'm using SocketServer without experiencing this problem - I can send any amount of data through without any problem.
However, I did have a problem at first, because I followed the example in the docs too closely. In the example, the socket object created in the onConnect is not set up as a 'persistent' object, it is only set up in the onConnect function, and when that function terminates, all references to the socket go away. This isn't immediately apparent because the socket continues to work until the garbage collector gets around to removing it. I could connect and send data, but then at seemingly random intervals the transmissions would fail. Once I figured out what the problem was I created a Socket object at the same 'level' I created the ServerSocket and fixed the onConnect function to assign the socket in the event to that object, it works perfectly.
Oops, sorry, i was on the wrong forum, thought you were talking about then new serversocket provided in the AIR beta 2.0
Turns out that The packets were coming through, only they were getting concatenated with the previous message. I checked the length of the received socket data and it showed that some messages were double the expected length.
I just read the data out as two separate messages in AIR.