PSQLException "FATAL: terminating connection due to administrator command" and "FATAL: the database system is starting up" errors in JBoss EAP

Issue

Encountering errors like below while using existing connections and attempting to obtain additional connections from the JBoss EAP pool.

... IJ000305: Connection error occured: ... org.postgresql.util.PSQLException: FATAL: terminating connection due to administrator command
...
... org.postgresql.util.PSQLException: This connection has been closed.
        at org.postgresql.jdbc.PgConnection.checkClosed(PgConnection.java:885)
        ...
...
... IJ000610: Unable to fill pool: java:jboss/datasources/MyDS: javax.resource.ResourceException: IJ031084: Unable to create connection
        at org.jboss.jca.adapters.jdbc.xa.XAManagedConnectionFactory.getXAManagedConnection(XAManagedConnectionFactory.java:531)
        ...
        at org.jboss.jca.core.connectionmanager.pool.mcp.PoolFiller.run(PoolFiller.java:97)
        ...
Caused by: org.postgresql.util.PSQLException: FATAL: the database system is starting up
        at org.postgresql.core.v3.ConnectionFactoryImpl.doAuthentication(ConnectionFactoryImpl.java:613)
        ...
        at org.postgresql.xa.PGXADataSource.getXAConnection(PGXADataSource.java:49)
        at org.jboss.jca.adapters.jdbc.xa.XAManagedConnectionFactory.getXAManagedConnection(XAManagedConnectionFactory.java:515)
        ...