MQ JCA adapter deployed to EAP 6.1.1 is consistently failing to recover transactions with 'ResourceException: IJ000655: No managed connections available within configured blocking timeout'

Issue

We are consistently failing to obtain MQ connections with the following error messages. This lead to the queue depth approaching 100,000.

WARN  [org.apache.camel.component.jms.DefaultJmsMessageListenerContainer] (Camel (camel-1) thread #273 - JmsConsumer[FOO.BAR]) Setup of JMS message listener invoker failed for destination 'FOO.BAR' - trying to recover. Cause: MQJCA1011: Failed to allocate a JMS connection.; nested exception is javax.resource.ResourceException: IJ000655: No managed connections available within configured blocking timeout (30000 [ms])