Connection manager not available during shutdown

The problem occurs when trying to access the database during the shutdown phase.
It looks like when our shutdown code tries to access the database - it is no longer available.

Our application is deployed as an EAR that has a SAR module to handle startup and shutdown.
We add our application specific startup and shutdown code in the corresponding MBean hooks.

In JBoss 7.0.2 and 7.1.1 we're encountering an error when the shutdown code is attempting to access the database and is failing due to the fact that the connection manager is closed:

13:08:37,975 ERROR [org.jboss.as.service] JBAS017200: Failed to execute legacy service stop() method: java.lang.reflect.InvocationTargetException
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) [rt.jar:1.7.0_01]
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57) [rt.jar:1.7.0_01]
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) [rt.jar:1.7.0_01]
at java.lang.reflect.Method.invoke(Method.java:601) [rt.jar:1.7.0_01]
at org.jboss.as.service.AbstractService.invokeLifecycleMethod(AbstractService.java:52) [jboss-as-sar-7.1.1.Final.jar:7.1.1.Final]
at org.jboss.as.service.StartStopService.stop(StartStopService.java:66) [jboss-as-sar-7.1.1.Final.jar:7.1.1.Final]
at org.jboss.msc.service.ServiceControllerImpl$StopTask.stopService(ServiceControllerImpl.java:1911) [jboss-msc-1.0.2.GA.jar:1.0.2.GA]
at org.jboss.msc.service.ServiceControllerImpl$StopTask.run(ServiceControllerImpl.java:1874) [jboss-msc-1.0.2.GA.jar:1.0.2.GA]
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1110) [rt.jar:1.7.0_01]
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:603) [rt.jar:1.7.0_01]
at java.lang.Thread.run(Thread.java:722) [rt.jar:1.7.0_01]
Caused by: java.sql.SQLException: javax.resource.ResourceException: IJ000451: The connection manager is shutdown: java:/org.test.NonSecureDS
at org.jboss.jca.adapters.jdbc.WrapperDataSource.getConnection(WrapperDataSource.java:137)
at org.test.StartupService.updateStatus(StartupService.java:37)
at org.test.StartupService.stop(StartupService.java:56)
... 11 more
Caused by: javax.resource.ResourceException: IJ000451: The connection manager is shutdown: java:/org.test.NonSecureDS
at org.jboss.jca.core.connectionmanager.AbstractConnectionManager.getManagedConnection(AbstractConnectionManager.java:321)
at org.jboss.jca.core.connectionmanager.tx.TxConnectionManagerImpl.getManagedConnection(TxConnectionManagerImpl.java:368)
at org.jboss.jca.core.connectionmanager.AbstractConnectionManager.allocateConnection(AbstractConnectionManager.java:464)
at org.jboss.jca.adapters.jdbc.WrapperDataSource.getConnection(WrapperDataSource.java:129)
... 13 more