one admits to being a failure; admission of anything is to allow it into somewhere. Except admission of guilt, I suppose. Well, no, even then admission of guilt is allowing guilt to enter into your mind/being, so I stick by my first point.
But it isn't a good way to say it - it would be better to say "she admits to being a failure", or "her admission that she is/was a failure".
Thanks ladies. Deadline was last night so replies were sadly too late, but I left it as 'admission of being' cos I found lots of examples of that being used on Google. A frightening way to get the 'right' answer on a paying job, I know!