Receiving "Interrupted while requesting permit!" when getting JDBC connection in JBoss EAP

Issue

We are observing an exception when connecting to our database. This is the root caused-by of the exception we're seeing:

 Caused by: javax.resource.ResourceException: Interrupted while requesting permit! Waited 0 ms
     at org.jboss.resource.connectionmanager.InternalManagedConnectionPool.getConnection(InternalManagedConnectionPool.java:309)
     at org.jboss.resource.connectionmanager.JBossManagedConnectionPool$BasePool.getConnection(JBossManagedConnectionPool.java:538)
     at org.jboss.resource.connectionmanager.BaseConnectionManager2.getManagedConnection(BaseConnectionManager2.java:348)
     at org.jboss.resource.connectionmanager.TxConnectionManager.getManagedConnection(TxConnectionManager.java:330)
     at org.jboss.resource.connectionmanager.BaseConnectionManager2.allocateConnection(BaseConnectionManager2.java:403)
     at org.jboss.resource.connectionmanager.BaseConnectionManager2$ConnectionManagerProxy.allocateConnection(BaseConnectionManager2.java:850)
     at org.jboss.resource.adapter.jdbc.WrapperDataSource.getConnection(WrapperDataSource.java:90)
     ... 43 more