You could use
Record button while playing and watching the stream in VLC, but this way you will not have the complete 11:59 stream recorded, because it is not possible to press the Record button before start of playback and so you have to do it during the playaback.
You better follow this with "Dump raw input" option ticked there:
Media > Convert/Save... > Network tab: to put video mms url > Convert/Save button > Destination file; [v] Dump raw input > Start button
If you do that, you will not see any progress in VLC player, but the "Play/Pause" button is pressed. It is quite confusing, so better if you also have Status Bar activated: View > Status Bar. There you can see following information: "Streaming". You will have to wait all 12 minutes. If you check the destination file during the process, you will see increasing its size.
If you want to download and watch it at the same time, then you should use another method:
Media > Stream...
It is similar but there are more options.
> You just check [v] Display locally and [File] Add
> Choose [Video - WMV + WMA (ASF)] profile, but disable
[ ] Activate Transcoding
> Then you can edit "General stream output string" and correct the filename extension .wmv instead of .asf if you wish so.
I hope, that all is clear now and you are able to save the stream by yourself.