I have two boys who faced similar issues.
My elder boy had been on the A lax team in town until 6th grade when he was put on one of two B teams. He was devastated and wanted to quit. My wife and I prevailed upon him to stick it out. He worked out on his own for at least an hour a night. As it turned out, a few months later, he tried out for an made a select travel team that some of the town's A players made and others did not. While he wasn't the best on the travel team, both experiences showed him that he needed to work hard if he wanted to be competitive an excel. He worked on his foot speed and worked on his stick skills. Three years later and he was made captain of the JV team at the high school as a Freshman!
My younger son on the other ahnd has seemed to always be lucky and made whatever team he tried out for. Except for last year when he tried to make a select summer travel team. All of his friends who tried out made it, but he did not. When he learned that he didn't make the team, he was depressed and angry. We pointed out his older brother's experience and pointed out that he should take this experience as a lessen that he needs to improve himself if he really wants to succeed. He spent the next six months running around the track and throwing against the lax wall. He also worked on his groundball skills. This fall, he made the team he was cut from and was also asked to join another select travel team, but chose instead to be with his friends on the first.
The mom in the article talked about her son regaining his confidence and his love of the game. We as parents can encourage our children to either be defeatist or face up to challenges and enter life with confidence.