You might take a look at this thread. We observed these types of issues start happening after Mavericks dropped. The problem where a connection is established, and then all the sudden drops is related to the Macs not playing well in an enterprise environment where routers running high availability protocols are in use. The fix is to modify the sysctl entry for unicast ARP requests:
$ sudo sysctl -w net.link.ether.inet.arp_unicast_lim=0
net.link.ether.inet.arp_unicast_lim: 5 -> 0
(you can set this also in /etc/sysctl.conf)
This disables the unicast ARP requests.
The details of the thread can be found here: Mavericks and Failed ARP causing network drops!
We also noted that some users computers seem to revert the change after a reboot, so we have started pushing the change to our users via our internal management system ever two hours.