There is definitely no limit of connections to any particular port in AIX ... I have loads of boxes with 2500+ connections to the port of the oracle listener.
I assume you are using connection pools to access somehow a database. If this is the case, please have a look here
Configuring and Using WebLogic JDBC
When your applications attempt to get a connection from a connection pool in which there are no available connections, the connection pool throws an exception stating that a connection is not available in the connection pool. To avoid this error, make sure your connection pool can expand to the size required to accommodate your peak load of connection requests.
To set the maximum number of connections for a connection pool in the Administration Console, expand the navigation tree in the left pane to show the Services—>JDBC—>Connection Pools nodes and select a connection pool. Then, in the right pane, select the Configuration—>Connections tab and specify a value for Maximum Capacity.
Kind regards
zxmaus