I am really irritated on this whole apartment situation here in switzerland. Even if you would be a perfect candidate and really need a place, you cant get anything! I dont know whats going on. All I know, is that it feels hopeless, especially for those who cant afford too much.
Keep at it. See more places, expand the area (maybe up the budget, or consider smaller places) apply to more places - be very open with people showing them and tell them that yes you really want the place and you would be the perfect candidate... We were all there and it will work out!