I have this same problem. I haven't found a solution anywhere, but a great workaround is using the Fader Start function - basically the moment the fader is slid into the main mix, the deck which you enable will start to play the tune. Hit the mode button, then select control, and turn on Fader start. It's actually really cool and allows you to do some ballsy mixes :) The deck will pause (or cue depending on the setting) once you bring it back.

I has the same problem with deck b on one I bought off eBay. The problem turned out to be the micro switch which us under the play button. I disassembled the unit (took ages) and swapped the play switch with the queue one (which doesn't get used as much).

Isn't the track loading when you hit the stutter start button the first few times? While it's loading, you can't start that song.
Koen