I believe these are all the same bug:
http://www.jeroenwijering.com/?thread=12001
http://www.jeroenwijering.com/?thread=11842
http://www.jeroenwijering.com/?thread=11646
http://www.jeroenwijering.com/?thread=11028
There seemed to be some misinformation floating about on those threads that somehow the MP3 file was to blame. But this is definitely not the case. Here is an example page of the same MP3 file being played with two different players:
http://mollyrocket.com/player/test.html
On the top is JW Player. Hit play on it, wait for it to load the whole file, and then try to slide the play-cursor around. You will see that you cannot move past the half-way point.
On the bottom is another Flash-based MP3 player. Hit play on it, wait for the loading bar to complete, and then slide the cursor around. Everything works perfectly.
Now, if you play around with the JW Player's seeking behavior, you can see exactly what is happening: clicking in the first half of the bar seeks to _twice the location you click_. So if you click a quarter of the way across the bar, you actually seek to the midpoint of the MP3. This produces another really strange behavior, which is that if you let the MP3 play to completion from where you seeked, it will still play the rest of the file correctly, but the play cursor will constantly be in the wrong place proportional to how close to the beginning you started. This is because the play cursor still _moves_ at the correct rate.
Truly bizarre! I'm guessing there must be some divide-by-two error somewhere in the seek code?
- Casey

Thanks for the clear demo! I took a look at this, and found something strange.
There is indeed a bug in here. The Sound API from Flash sometimes indeed stops and sends COMPLETE calls to the player, even though the sound isn't done yet. This is with a combination of:
1. actionscript3 (that's why the other player works - it is in AS2).
2. a certain version of the plugin > 9.0.28.0 (I don't know the exact version, but the bug IS there in 0.115 and 0.124).
I tried a couple of workarounds, e.g. ignoring the COMPLETE calls when I'm sure the sound has not ended yet. No luck though, since the Sound API simply drops.
Anybody has some additional insights? Else it seems to be time to file a bug with Adobe...