MySQL/Hibernate - How do I debug a MySQL pooled connection that keeps dropping?

From the stack-trace you provided, I can draw a single conclusion: you are simply running out of connections.

This can be caused by long running transactions, possibly due to slow queries or improper application transaction boundaries.

I suggest you start using FlexyPool, which supports Tomcat DBCP and get a better understanding of both the connection and transaction usage. FlexyPool provides many histograms you might be interested in, like connection acquisition time and lease time.

An, just to be on the safe side, check the MySQL driver version too and see if you're running on an outdated library.

Hibernate errors are a bit abstract and sometimes it can be tricky to find the bug by the stack trace. I think that may be a problem of your application, maybe you're not closing Hibernate connections properly on some cases or your application may have a memory leak.

Have you tried to monitor the application with jconsole from the JDK?

You can set this on your Tomcat configuration console in the Java arguments (I'm assuming you're using Tomcat), to enable the jconsole

-Dcom.sun.management.jmxremote
-Dcom.sun.management.jmxremote.port=8086
-Dcom.sun.management.jmxremote.ssl=false
-Dcom.sun.management.jmxremote.authenticate=false

Then connect to a remote process for example

localhost:8086 

and watch the threads as you go thru the operations that make the application stop.

Edit

If you're not using Tomcat and you're running your application in a Windows environment you can monitorize the threads using for example Process Explorer and monitorize your application.