In "Two Kinds" by Amy Tan, why might Jing-Mei's mother want her to keep playing the piano even after her dissastrous performance?

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Jing-mei’s mother wants her to continue playing the piano because if Jing-mei stops, she has won.  Her mother wants an obedient daughter.  She also has not given up on the idea that her daughter will be a success.

Jing-mei’s mother wants her to be some kind of prodigy.  At first she is not sure what kind.  They “didn't immediately pick the right kind of prodigy” and her mother tried singing, dancing, and memorization first.  Then she saw a little girl playing the piano on television. 

And then I saw what seemed to be the prodigy side of me - a face I had never seen before. .. The girl staring back at me was angry, powerful. She and I were the same.

Jing-mei promises herself that she will not become what she is not.  She agrees to take piano lessons, but as soon as she realizes that the piano teacher Mr. Wong is deaf, she does not try.  She pretends to learn to play.

…I was so determined not to try, not to be anybody different, and I learned to play only the most ear-splitting preludes, the most discordant hymns.

Jing-mei’s mother does not give up.  She is just as stubborn as Jing-mei.

 [My] mother walked in and went straight to the back, into the bedroom. No accusations, No blame.

Jing-mei is frustrated and somewhat disappointed when her mother does not shout, but she finds out why two days later when her mother drags her to the piano bench and forces her to play.  If she gives in, her daughter has not been obedient and she has failed as a mother.

Only two kinds of daughters," she shouted in Chinese. "Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"

In the end, she gives in only when her daughter hurts her so badly, by insisting that she wishes she was dead, that she no longer has the will to fight.

Jing-mei's mother had a difficult life.  She wanted better for her daughter.  She regretted the death of her twin babies, and could not understand how her daughter could use them against her.  She has lost faith and understanding in her daughter.