Microsoft SQL Server "connect timed out" failure in JBoss EAP

Issue

com.microsoft.sqlserver.jdbc.SQLServerException: The TCP/IP connection to the host <HOST>, port <PORT> has failed. Error: "connect timed out. Verify the connection properties. Make sure that an instance of SQL Server is running on the host and accepting TCP/IP connections at the port. Make sure that TCP connections to the port are not blocked by a firewall.".
        at com.microsoft.sqlserver.jdbc.SQLServerException.makeFromDriverError(SQLServerException.java:190)
        at com.microsoft.sqlserver.jdbc.SQLServerException.ConvertConnectExceptionToSQLServerException(SQLServerException.java:241)
        at com.microsoft.sqlserver.jdbc.SocketFinder.findSocket(IOBuffer.java:2243)
        at com.microsoft.sqlserver.jdbc.TDSChannel.open(IOBuffer.java:491)
        at com.microsoft.sqlserver.jdbc.SQLServerConnection.connectHelper(SQLServerConnection.java:1309)
        at com.microsoft.sqlserver.jdbc.SQLServerConnection.login(SQLServerConnection.java:991)
        at com.microsoft.sqlserver.jdbc.SQLServerConnection.connect(SQLServerConnection.java:827)
        at com.microsoft.sqlserver.jdbc.SQLServerDriver.connect(SQLServerDriver.java:1012)
        at org.jboss.jca.adapters.jdbc.local.LocalManagedConnectionFactory.getLocalManagedConnection(LocalManagedConnectionFactory.java:328)
        ...