ActiveMQ stops 'talking' - apache-camel

Question

We have an OSGi (Karaf 4.0.5) server that uses Camel 2.15.4 & ActiveMQ 5.12.0 for remote calls to services within the server.
After the server has been up for several weeks ActiveMQ sometimes appears to stop taking any new connections from outside the server. Remote clients attempt to make connections, but they eventually just time out.
The problem is we don't even know where to start looking for what the problem might be. There are no specific errors in the server log that seem to pertain to ActiveMQ or Camel.
We can log in to the Karaf console and do a activemq:bstat, but we have hundreds of queues for all the services, so it's like a needle in a haystack, and we don't know what the needle looks like.
Can someone please tell us what things we should look out for?
ActiveMQ XML config:
<broker xmlns="http://activemq.apache.org/schema/core"
useJmx="true" brokerName="${broker-name}" dataDirectory="${data}" start="false">
<destinationPolicy>
<policyMap>
<policyEntries>
<policyEntry topic=">" producerFlowControl="true" memoryLimit="1mb">
<pendingSubscriberPolicy>
<vmCursor/>
</pendingSubscriberPolicy>
</policyEntry>
<policyEntry queue=">" producerFlowControl="true" memoryLimit="1mb">
</policyEntry>
</policyEntries>
</policyMap>
</destinationPolicy>
<managementContext>
<managementContext createConnector="false"/>
</managementContext>
<persistenceAdapter>
<kahaDB directory="${data}/kahadb"/>
</persistenceAdapter>
<plugins>
<timeStampingBrokerPlugin futureOnly="true"/>
</plugins>
<transportConnectors>
<transportConnector name="tcp" uri="tcp://localhost:4210"/>
</transportConnectors>
</broker>