Is it possible to specify a particular source port for Modbus TCP connections? I am connecting to some fussy equipment that gets upset when Ignition frequently changes the source port it connects with.
No, TCP/IP generally doesn't permit that. It won't happen, though, if the connection doesn't break or time out. Have you used Wireshark to see what is really going on?
(Many Modbus devices will close an idle connection after ten seconds.)