This is one of the main reasons why I like the Spring Framework. Spring can wrap that system and eliminate the tiresome and (as you have seen) error-prone process of obtaining and releasing connections.
If you were using
Tomcat, I'd recommend that you look at the Apache DBCP settings. DBCP is the plug-in that comes with Tomcat for database connection pooling and it has several configuration options that help find and manage connection leaks.
I've never had to go that deep into WebLogic, however. I'm not sure what they're currently using for connection pool management, so I suggest that you check their documentation and/or ask in the WebLogic forum.
In fact, I'll try and move this question over there, since there's nothing JSF-specific in this question.