Have you tried measuring the time it takes to execute SQL over JDBC for the situation, and also measuring execution speed for rest of critical code? You may need to put in code to test it.
It sounds like there is a leak somewhere causing the SQL execution to slow down - a guess, but you need to do some more investigation. You may want to see if you can get anything useful from a thread dump from the JVM:
kill -QUIT process_id
Other things to try are other JDBC drivers.