DevOps, CI/CD and Automation

Hi all ,
I have a application that interfaces via the ODBC client.
During a data process run, but after initial connections and a small ( less then 500 ) queries have run,
I keep getting "ORA-12516, TNS: listener could not find available handler with matching protocol stack"
Having the application retry the connection allows processing to continue for at least one statement, or for what seems to be a random number of statements. Often as many as 90,000 ( the end of the test data set I am working with ).
The application uses a persistant connection, And I can see the session is still open on the server despite the error, In fact I am totally unable to see any change on the server, once the error is cleared I see no new sessions open, no new cursors, nothing except statements begin to process again.

I am assuming the error to be on the server side, because all connected clients report the error at the same time.
The error seems to be related to the number of active clients that are connected at a given time, two or more active clients will cause the error about 50% of the time, while 3 or more active clients will cause 75% of the time.

Any Ideas at all would be helpful.
Thanks.
--Bill