I'm a Flash developer. If you can point me at where I can find the source code, I can check that out. I expect it was made using Flash MX (6) and its MP3 handling isn't as tolerant as later versions and you have to do a lot of error handling to make it more stable.
It's also not too good with non-standard MP3 files. If you check out the 'advanced' method of creating MP3 files on moodle docs, they explain it quite well there. Basically you have to make sure that the audio WAV was recorded at 44.1 khz (sampling rate, not bitrate).
If you can find a good CODEC to recode your MP3 files you can iron out all these reliability 'wrinkles'. It's not really applicable in this case, but Flash can't handle MP3 bitrates higher than 128 kbps.
And yeah, if you can't do it in Flash, there are plenty of other options: Quicktime, Windows Media Player and RealPlayer but RealPlayer is less common than the others.