My code is actually producing the next error:

org.apache.axis2.AxisFault: Timeout waiting for connection
    at org.apache.axis2.AxisFault.makeFault(
    at org.apache.axis2.transport.http.HTTPSender.sendViaPost(
    at org.apache.axis2.transport.http.HTTPSender.send(
    at org.apache.axis2.transport.http.CommonsHTTPTransportSender.writeMessageWithCommons(
    at org.apache.axis2.transport.http.CommonsHTTPTransportSender.invoke(
    at org.apache.axis2.engine.AxisEngine.send(
    at org.apache.axis2.description.OutInAxisOperationClient.send(
    at org.apache.axis2.description.OutInAxisOperationClient.executeImpl(
    at org.apache.axis2.client.OperationClient.execute(

After extensive searching the answer seems to become here:

Except I am unable to access http client directly (that's completed in auto produced code).

Rather I've attempted:

Which appears to assist slightly. Nevertheless it only delays the issue I usually obtain the timeout. Even the instructions seem to be to have an old version of Axis since Axis2 doesn't have AxisProperties. I'm using version 1.5.1. Any suggestions?

I believe it was a bug, see here and it has been fixed with Axis2 1.5.2 (a minimum of for produced code). With custom code, you have to tackle this issue by hand.