This week's book giveaway is in the Other Open Source APIs forum. We're giving away four copies of Storm Applied and have Sean Allen, Peter Pathirana & Matthew Jankowski on-line! See this thread for details.
I've never needed a tool to do this as I use a framework that handles closing resources for me. It would be equal effort to go through the tools (google the categories I listed) to find out which ones support your requirement. Or maybe you'll be lucky and someone who sees this Monday will have had the same requirement as you and knows the solution off the top of their head.
For FindBugs, you already know the name of the tool making it easy to find this information. FindBugs has the list of rules online. The ODR ones look like what you need.
The Apache dbcp connection pooler can be configured to take a stack snapshot when you acquire a connection. The snapshot is then saved, and if you end up with leaks, it can be dumped, so you'll know where it was opened.
However, the ability to ensure that connections don't leak is one of the primary reasons I use the Spring Framework to manage my persistency layers. I've seen too much hand-written code that forgot to free up stuff when an unexpected SQL exception was thrown.
Customer surveys are for companies who didn't pay proper attention to begin with.