Now this is an interesting thread. There's a lot of interesting thinking on an interesting subject.
The doppler effect can make the perceived pitch go up and down as, for example, a train or fire truck whooshes by:
http://www.windows.ucar.edu/tour/lin...er_effect.html
It's certainly not in contradiction of the laws of thermodynamics or any such thing. But on the other hand I certainly wouldn't expect this to take place in a home stereo or headphones, unless your stereo is blaring like a freight train and whizzing by at 50 miles per hour.
Also, if you hit a note hard on the piano, guitar, drum, and other similar instruments, the pitch will start out just a little higher and then settle down to a steady very slightly lower pitch. You can hear this if you listen closely while tuning a guitar, for example, or using an electric guitar tuner and watching the pitch start just a little high and then settle down to the correct pitch. But you are talking just shades of a pitch, to someone whose ears are sensitive to fractions of note intervals, not going up and down from one note (half step) to another. And this has little or nothing to do with what goes on with headphones or a home stereo.
Headphones and speakers do have resonances that I think could be subjecively perceived as a lack of "decay." The extreme of this could be one of those kids' mechanical echo microphones where a spring-loaded chamber creates a reverb/echo type effect. Also, if there's just plain too much bass, that could mask what's going on in the highs, resulting not hearing what's going in the highs well enough, which you might subjectively perceive as a lack of decay.
As far as a headphone or speaker having too fast of a decay, that is hard for me to explain or imagine. You want a lack of resonances and a smooth frequency response. Maybe if the highs were too emphasized things would sound a little too sharp or crisp, resulting in what could be pereived as a too fast decay. You'd hear an emphasis on sounds in the uper end of the audio spectrum, that are sharp and crisp and go away fast. That would really be a frequency response problem.
Just my random thoughts....