Please let me know the following details to help you better:
1. Are you using a custom board or superspeed explorer kit?
2. If it is a custom board, then is it bus powered or self powered?
3. By "shut off my computer", do you mean to say that you are turning off the computer?
4. Which firmware are you using for the test? Is it an SDK example project? If not please share the code so that I can have a look at it.