The difference is in meaning in first sentence says I've been asking YOU all day means that "all day long i was busy in asking you" something. for example questions. but in second sentence it says I've been asking FOR YOU all day which means that what i was doing all day long was because of you.for example: i have been asking train tickets for you all day.

I've been asking you all day means you have been asking that person all day a question, usually permission or to get the person asked to do something. I've been asking for you all day means you have been asking other people all day where the person in question is.