How does Apple AppStore rank search results?
I'd venture to guess and say that the App Store ranking algorithm is a company secret, much like Google's web search rankings. It seems to me that the radical changes in placement you are witnessing are as much the fickleness of App Store customers as anything else. 

Correlation isn't causation by any means, but it seems fairly clear by your description of the events that if you want a lot of downloads you will either have to make it free (and perhaps ad-supported?), or your alarm clock app needs to do something so unique amongst the plethora of alarm clock apps that customers will feel compelled to pay for it.