Identifying importance of each feature in deep model
This could mean that your features are heavily correlated. As a result, when you set one variable to 0, there is always another one that carries the same information. 
Try to set several features to 0 to see if you have the same issue. If yes, then it might be something else (maybe your code).

You might also be interested in this paper, you'll find several methods to assess feature importance.