There are many reasons IMO that athletes go broke:
1)Small Earnings Window: (as Hive account@rymlen has mentioned)

While the more traditional careers may allow a person to work 30 to 50 years, a professional athlete will work only a fraction of that time.

2)Lack of Financial Knowledge:
According to "Sports Illustrated," most athletes lack the financial knowledge to manage the large sums of money they're earning. Allen Iverson is one of the many athletes who lived a lifestyle based on his peak earnings, yet failed to think about the money he would need later in life.

3)Extravagance (Show off)
any of the athletes who find themselves bankrupt overspent on extravagance only to find their possessions nearly worthless later in life.