A lot of the almost magical ability of children to learn is chemical in nature.
The brain chemistry of children is simply different from that of adults. There is a lot more acetylcholine. Research has been done with animals that confirms that the most basic cognitive abilities cannot only be learned through increased amounts of acetylcholine, but they can also be *unlearned*.
Experiments with cats has shown that cats can unlearn and relearn depth perception through injections of acetylcholine into the brain. (Even though I use this as an example, I think these experiments are horribly inhumane.)
As time goes by, however, I do think that performance anxiety has a lot to do with lack of progress, lack of learning. When you take a human being and consign them to the role of a machine (your purpose is to produce, perform), you quite naturally get bad results.
It's inhumane, really. I've always found it hard to deal with.
Learning can be a joy when it isn't something you have to do for some purpose. It's best when it's done for its own sake. I think we learn best, then.
The very fact that productivity is demanded of us is what makes us unproductive. If performance were not tied into feelings of worth to one's self, family, community, country, etc., we'd see a lot less procrastination and escapism, I think.
Of course, a world without such demands is just an escapist fantasy.
That being said, whenever I talk to my nephew (whom I love very, very much) I always try to let him know I understand his feelings and that I love him very much ... that his performance isn't what makes me love him, it's just him. I love him for who he is. It is my hope to inform him that he doesn't need to feel he has to do x, y, or z to be a good person, to be loved and valuable.
IAM2, I think what you're doing wih your daughter is wonderful. It must be hard that you can only spend 2 hours with her a day 
