A.B.
In general I would say that your daughter is very sensitive by nature and is easily hurt by others. It is wonderful to be sensitive (as it will help her to develop compassion and empathy) but it is very hard to overcome those first knocks and bruises that teach us that the world isn't all sunshine and flowers. She needs help in building her confidence and in overcoming failure so she can see that despite what the world has in store for her, she is still a valuable and important person.
I would start by helping her build some confidence. We should always be careful about negatively labeling our children (I have read that we may not need to build confidence in our children as much as we need to stop stealing it from them.) and always respond to their needs with gentleness, respect, compassion, and love. Think of the kind of person that your daughter is, how could you help her build her confidence? Is there something she enjoys but does not feel particularly good at that you could help her develop? If she is not much of an artist, but enjoys the process, get her some paints and an easel and praise all her work. Make her feel special for what she can do and praise all her attempts to do better. Have her try new ideas and projects and tell her how proud you are of her for trying. Give her some responsibilities around the house that show her that she can do many things.
The next step would be to help her overcome failure. Usually children know they have failed and don't need to be told. We should help them find out what went wrong and encourage them to try again. Praise the effort and help them realize that we won't always win the game, but if we don't try we will NEVER win. Help her to realize that even when she makes mistakes, her friends will still like her and she will still be a good person. We don't always have to win. Help her to use her compassion to see what others would feel like if she always won and they never got to win. Ask her how it feels to win? How many people won? Isn't it nice that they got to feel like a winner? Ask her how it feels when she loses, how many other people did not win? Does everyone who doesn't win feel bad? Would they be sad if you won everything and they never got to win? Everyone has some things they are good at and some things they need to improve on. Help her to understand that we have these different talents so that everyone has a chance to win at something. And remind her that she will never win, never get any better, and never have fun with her friends if she refuses to try. Then let her make the choice. Does she want to try and be happy even if someone else gets to win? Or does she want to wait and play another game? Eventually, with your encouragement, she will learn to accept that she can't always win.