Some Quicktime files are protected at the time of creation by the author of the video - you can create an .mov with protected audio (this was implemented with Quicktime 5 - and if you have Quicktime 4 the audio protection does not work). This is often done with trailers and other files that people want to protect in some way. If the audio is protected, the only you will be able to get it out is to first convert the file into another format.
If you install Quicktime 4 your Flash MX will probably pick up the audio.
If you're looking for free software, you can probably use the Windows Media encoder, but then you're converting it into .wmv which is not a good format to use for future conversion.
If you're willing to pay for software, there are a lot of other programs you can use.