Can you please provide more information?
What is the source of this music? What file format is it saved as?
If you output a WMV or AVI of your video, does the music play in your shared video?
This is aimed at Premiere Pro, but may help
A link with many ideas about computer setup http://forums.adobe.com/thread/436215?tstart=0
Work through all of the steps (ideas) listed at http://ppro.wikia.com/wiki/Troubleshooting
If your problem isn't fixed after you follow all of the steps, report back with ALL OF THE DETAILS asked for in the FINALLY section, the questions at the end of the troubleshooting link... most especially the codec used... see Question 1
Along with the answers to the questions (source footage specs. are very, very important), can you detail any editing that you have done in PrE? One area to consider is any work with the Audio Mixer, that might apply automated Track Keyframes. If done improperly, this can cause exactly what you describe.
Also, exactly where are you encountering the Audio attenuation?
I had the same problem in Premiere Pro and it turned out that I needed to render the timeline.