Question:
you know how on most perfume bottles there's the spray mechanism and the ring around it that you sort of push the spray mechanism into? does that make any sense? like you have the sprayer and the donut shaped thing that it stands inside? i think maybe the seal between these two is not airtight and this is how air gets in. but of course when i tip it outside no fragrance pours out, so maybe i'm wrong. but i agree, the bottles are not so carefully put together as to be airtight

Answer:
My bet is that outside air enters the bottle during the recovery phase of the spray stroke.
One way would be to employ a very simple one way 'bladder', normally closed over a hole in the inside of the spray/cap mechanism, that would keep liquid in the bottle even when turned upside down, while only allowing air in to equalize pressuren and never allowing air or liquid to escape the bottle through the hole. Then a return to a position that prevents both air coming in and liquid going out such opening would seal the bottle again, until another a vacuum is formed inside by spraying, to move the bladder and open the hole for air to enter again.

Answer:
This is easily the most insane thread I've ever seen.
I'd guess that maybe the air seeps in slowly through the seal gradually as the vaccuum inside increases.
I think picking it up and using it does just about all the mixing that may be required.

Answer:
Ultimately I mostly agree with MadScientist. Shaking a cologne does not make much difference for the typical fragrance user. It makes about as much sense as keeping your fragrances in some form of refrigeration. For the typical user who uses up their fragrance within a few years of purchase, it is really does not make sense to worry about it. For people with a significant investment in many expensive fragrances who want maximize the shelf life, I feel it is a genuine consideration, especially for fragrances with a splash application rather then spray.