I don't know anything about physics, but here's a stab in the dark. What about the stars own gravity. What if the matter is being dragged along by the stars gravity, only at a slower rate than the star is traveling? We are so far away it just appears that the matter is not moving. When in fact the star is draggin it keeping the discarded matter really hot.

Also from the pic it looks like it is traveling through something, disrupting some field or gas we cannot see. Kind of like a rock passing through water or thick smoke. If you look closely at the pic you can see some distinct rippling affects and even a spiral affect close to the tail of the star. Something is distrupting the flow of that matter. Another gravity field produced nearby perhaps? Maybe not.

So the rate of decay would be slow as the star drags along the matter keeping it hot and whatever it is passing through providing the constant fuel to maintain the burn. Over time the matter slowly decelerates, cools and fades from our vision.

All in all it is still a guess.