Ainda estou recebendo tempos limite do JDBC depois de tentar configurar o c3p0 seguindo todos os exemplos que pude encontrar. Estou usando JPA, Hibernate, Tomcat, MySQL [AWS RDS]. Aqui está o trecho de persistence.xml:

<property name="javax.persistence.jdbc.url"
value="jdbc:mysql://url..." />
<property name="javax.persistence.jdbc.driver" value="com.mysql.jdbc.Driver" />
<property name="hibernate.dialect" value="org.hibernate.dialect.MySQLDialect" />
<property name="connection.provider_class"  value="org.hibernate.connection.C3P0ConnectionProvider"/>
<property name="hibernate.c3p0.acquire_increment" value="4" />
<property name="hibernate.c3p0.idle_test_period" value="3000" /> 
<property name="hibernate.c3p0.max_size" value="100" />
<property name="hibernate.c3p0.max_statements" value="15" />
<property name="hibernate.c3p0.min_size" value="5" />
<property name="hibernate.c3p0.timeout" value="100" /> 

E o log de erros:

09:18:51.776  WARN   org.hibernate.util.JDBCExceptionReporter  - SQL Error: 0, SQLState: 08S01
09:18:51.777  ERROR  org.hibernate.util.JDBCExceptionReporter  - The last packet successfully received from the server was 38,491,585 milliseconds ago.  ...