As cheng points out, grab the connection and release the connection at start/exit of your business methods and you should be on your way. Your connection pool should give you a clean connection for the given backend based on the DataSource you are using and there is zero reason that each EJB has a specific connection object, other than a connection object for backend that you are accessing.
[Message sent by forum member 'lancea' (lancea)]
http://forums.java.net/jive/thread.jspa?messageID=241574