We have a piece of software (webapp with Tomcat) using Apache commons connection pooling, and worked great for years. In the last month I had to update the libraries due to an old bug we were encountering. The bug had been fixed in a recent version.
Shortly after deploying this, we started getting exactly these messages. Out of the thousands of connections we'd get a day, a handful (under 10, usually) would get this error message. There was no real pattern, except they would sometimes cluster in little groups of 2 to 5.
I changed the options to on the pool to validate the connection every time one is taken from or put back in the pool (if one is found bad, a new one is generated instead) and the problem went away.
Have you updated your MySQL jar lately? It seems like there may be a new setting that didn't used to be there in our (admittedly very old) jar.
I agree with BalusC to try some other options on your config, such as those you're passing to MySQL (in addition to the connection timeout).
If this failure is transient like mine was, instead of permanent, then you could use a simple try/catch and a loop to keep trying until things succeed or use a connection pool to handle that detail for you.
Other random idea: I don't know what happens why you try to use a closed connection (which exception you get). Could you be accidentally closing the connection somewhere?