It's because it does not have set in sleeve and it has a loose, boxy fit.
A traditional classic polo with set in sleeve would stay up. The neckline would flatter short hair/ long neck, but you might or might not like the style -- it would appear classic/ preppy and would. need to be juxtaposed to more unusual items to work for your style.
This is a really fun, pretty top, but the kind I run from as fast as I can for exactly this reason. For me, the fuss factor would be the kiss of death. My shoulder line is square -- but my bone structure is small and the shoulder area is not broad. And my bust is relatively small. So tops like this will slip and slide all over the place.
Other tops that I have to watch -- wide boat necks without set in sleeves. I love the look of a boat neck but if the neckline is too wide or the sleeve is not neat, it won't work. It will look nice if I'm standing still (i.e. it will flatter well enough) but it will drive me bananas.
This is also why I need to watch all the oversize looks very very carefully. I love a batwing, a dropped shoulder, etc. etc. and some of these styles can indeed work well on me -- but I have to be super careful about the details of fit.