Network Render - Connection Reset by Peer

Hi,
I’m trying to set up 52 machine on my school network to render a cycles animation.
We are using Macs all running OS10.9.
All machines have Blender 2.71.

I manage to set up Master and Client and about 20 Slaves, then after that as I add more slaves, I keep getting messages on different machines saying ‘connection reset by peer’ and they drop out of the list of Slaves.
The job I am sending is a Cycles animation. I’m distributing in chunks of 1.
I seem to be unable to get all 50 Slaves going at once. As Slaves drop out - they return a blank image back to the Client, and an error is added to the list in the Master Monitor.

I do have even more desktops to add to the Slave list - but as i don’t seem to be able to get more that 20 machines working at one time, there’s little point.

Is this a known problem?
Is there a limit to the number of Slaves?
Any help would be appreciated.

Thanks.