Intermittent SQLException "org.apache.commons.dbcp.PoolablePreparedStatement with address: "..." is closed." in AMQ broker, causing broker to shut down

Issue

We intermittently face the following warning in our AMQ log files:

WARN  | 99.1:55704@61616 | JDBCPersistenceAdapter | 219 - org.apache.activemq.activemq-osgi - 5.11.0.redhat-630224 | 
JDBC Failure: org.apache.commons.dbcp.PoolablePreparedStatement with address: "..." is closed.

This may be followed by

WARN  | MQ NIO Worker 10 | RegionBroker    | 162 - org.apache.activemq.activemq-osgi - 5.11.0.redhat-630187 | 
Caught an exception sending to DLQ: Message ID:XXX dropped=false acked=false locked=true

As a result the broker shuts down.
This happens although we don't see any problems with the connections to our database.