Can iPad remember my password of apple id?

This prompt is a security feature to prevent anyone from picking up the ipad and making purchases or downloading anything that you might not want done. If you have a credit card attached to your itunes account and then "allow" it to not prompt you, then a friend or a child could open the app store or itunes and make multiple purchases that you might not want. I only get prompted when I make a purchase or download an update. If you are getting prompted otherwise it might signal that you have an app that is not able to finish downloading and keeps prompting you to get the authorization to do so.