Amazon Prime is entrenched in an exclusivity war. The company, which offers deals on shipping to members as well as streaming of television shows and movies, is in a fierce competition with sites like Netflix for more customers. For Amazon Prime, this means removing shows from their streaming list that are also available on other platforms, to keep their list exclusive.
Certain BBC shows, like Doctor Who, are also available on other streaming sites, so they will be removed from Amazon Prime starting on 15 February. The Verge says that,
“One of the easiest ways to help the video service stand out is to fill it with shows and movies that simply aren't available elsewhere, and accordingly sources say the company’s content focus in 2015 will be on original programming and exclusive content deals.”[Source: Hypable]