Web server is reaching the maximum connections (memory?)

Issue

In periods of peak load, we see the following exception from JBoss:

Caused by: java.net.SocketException: No buffer space available (maximum connections reached?): connect
     at java.net.PlainSocketImpl.socketConnect(Native Method)
     at java.net.PlainSocketImpl.doConnect(PlainSocketImpl.java:333)
     at java.net.PlainSocketImpl.connectToAddress(PlainSocketImpl.java:195)
     at java.net.PlainSocketImpl.connect(PlainSocketImpl.java:182)
     at java.net.SocksSocketImpl.connect(SocksSocketImpl.java:366)
     at java.net.Socket.connect(Socket.java:525)
     at java.net.Socket.connect(Socket.java:475)
     at java.net.Socket.<init>(Socket.java:372)
     at java.net.Socket.<init>(Socket.java:186)
     ...