I have attached pictures of my Airtime mount settings and my Mixxx mount settings that work when the output stream type is MP3. These same settings do not work when the output stream type is set to OGG/VORBIS. 

You are required to have a specific OGG mount point on your stream server (icecast)
Do you have it?

If not  (if you use a stream host asked them to list one for You)

If you can configure your own stream server follow these steps

sudo pico /etc/icecast2/icecast.xml

then scroll down to the mount definition section and do something like this

<mount>
    <mount-name>/airtimestream.ogg</mount-name>
</mount>

and
while you at it go to the top of the icecast.xml and change the number of source from 2 to say 4 (optional)
to read

<sources>4</sources>

Now restart your icecast service

sudo service icecast2 restart


Key points here is that

1. You need a specific mount point for the ogg stream .It must contain the extension (.ogg)
2. you cannot use the existing mp3 mount (/ices) you need another for OGG (/cream.ogg)
   
3. You might need to increase the sources if you use more than one in the stream settings

If you use any firewall on your computers,you must

1. Allow outbound traffic(port) on the stream port of the MIXXX computer
2. Allow outbound and inbound traffic (port) ie. both on the Streaming Icecast Server
   

Good luck

VOISSES

I am only working with one stream at a time to try to isolate the issue.  I have tested the MP3 stream type with every suggestion you made and others and every combination allowed me to successfully connect to the master mount.

<!-- Only define a <mount> section if you want to use advanced options,
         like alternative usernames or passwords
    <mount>
        <mount-name>/example-complex.ogg</mount-name>

        <username>othersource</username>
        <password>hackmemore</password>

        <max-listeners>1</max-listeners>
        <dump-file>/tmp/dump-example1.ogg</dump-file>
        <burst-size>65536</burst-size>
        <fallback-mount>/example2.ogg</fallback-mount>
        <fallback-override>1</fallback-override>
        <fallback-when-full>1</fallback-when-full>
        <intro>/example_intro.ogg</intro>
        <hidden>1</hidden>
        <no-yp>1</no-yp>
        <authentication type="htpasswd">
                <option name="filename" value="myauth"/>
                <option name="allow_duplicate_users" value="0"/>
        </authentication>
        <on-connect>/home/icecast/bin/stream-start</on-connect>
        <on-disconnect>/home/icecast/bin/stream-stop</on-disconnect>
    </mount>

   <mount>
        <mount-name>/auth_example.ogg</mount-name>
        <authentication type="url">
            <option name="mount_add"       value="http://myauthserver.net/notify_mount.php"/>
            <option name="mount_remove"    value="http://myauthserver.net/notify_mount.php"/>
            <option name="listener_add"    value="http://myauthserver.net/notify_listener.php"/>
            <option name="listener_remove" value="http://myauthserver.net/notify_listener.php"/>
        </authentication>
    </mount>

    -->

<mount>
    <mount-name>/airtimestream.ogg</mount-name>
</mount>

Key things here are that

1. the stream is enable (tick)
2. the username and password should be the same as the mp3 stream information

Give me some more information on what error you see when you try to connect.

As a last case try pushing a stream directly to the server  from mixxx or butt with the icecast credentials and post the access log and error log

VOISSES

My original post contained a sample of the error.log entries I get when I connect an OGG/VORBIS stream to the icecast server.  I have included samples of both logs when an OGG/VORBIS stream is connected. It looks like the connection is constantly dropping and reconnecting?  Do you know what the "0" and "1" at the end of the access log entries mean?

This is what the mounts look like in my icecast.xml file:

I also notice that if I check the Icecast admin page, "SERVER_IP":8000/admin/listmounts.xsl, no mount is listed when airtime's output stream type is set to OGG/VORBIS.  When the output type is set to MP3 and AAC, the Icecast admin page shows the mount, but when types OGG/VORBIS and Opus are used the admin page shows no mounts.  Interestingly Airtime shows the successfully connected message for all four output types.  So I will change the output type to OGG/VORBIS, click save, and airtime tells me:

<!--This is what your mount points should look like if you want a separate mount point-->

<mount>
        <mount-name>/live</mount-name>
    </mount>

    <mount>
        <mount-name>/mount</mount-name>
    </mount>

<!--You need an explicit mount for ogg like this -->
<mount>
    <mount-name>/airtimestream.ogg</mount-name>
</mount>

1. You must state an explicit mount point to use Ogg/vorbis
2. To use opus,your version of icecast must be >=2.4.0, check your version installed  (icecast2 -v).its normally 2.3.2
3. /mount  and its variant are for mp3 streams
4. /mount.ogg  and its variant are for ogg streams
5. You can only see a mount point on the status page when a connection is made
6. Your mount will lock up even when you push the wrong type mp3 or ogg and appear connected but unavailable.Please note my error statement above
   
7. Read this https://wiki.sourcefabric.org/display/CC/Airtime+Opus+Support to install opus on 12.04.I cannot tell if there are an Icecast 2.4.0 in the ubuntu/debian backports.
8. Remember to restart your icecast server if any change is made to icecast.xml

Good Luck

VOISSES

Same result as the mount without the ".ogg".   After I restart icecast, the Master source is disconnected as soon as I save the new settings in airtime.  The "airstream.ogg" mount never appears on the icecast admin page even though airtime says it's connected and clients can no longer connect to the master mount. 

error.log:

Also, I'm not interested in using Opus; I was just testing the other options to have comparable data.  :)

Ok I am a bit confused by your logs.
Is it a reduct version?

why is there a mount in liquidsoap here


This indicated that you are pushing 2 clients to the same mount point and therefore you will have issues with one

The OGG information is to be on the left side where the stream information is and not where the master is

Here is a my test to proof that it works

Is it a reduct version?

"why is there a mount in liquidsoap here


This indicated that you are pushing 2 clients to the same mount point and therefore you will have issues with one"

airtime-check-system results while OGG/VORBIS output stream is connected and verified to be working properly:

Still no luck.  I am going to take your advice and blow this whole server away and start fresh with Ubuntu 12.04.  Thank you again for all your advice VOISSES.  I'll let you know if I have any trouble with the 12.04 setup.