Finally, I found a message in the Forum, which describes the way to turn off the Connection Close Monitoring.
It works for me now.
But should CachedConnectionManager check the Connection auto commit setting before closing it?
(That is if auto commit is false, don't close the connection. And users are on their own to make sure everything is closed correctly.)
In the folowing file:
transaction-service.xml for 3.2.x
jbossjca-service.xml for 4.x
<!-- Enable connection close debug monitoring -->
Change setting to false.