Whenever I finish the seventh battle, I'm given BP and sent to the lobby. How do I continue my challenge after seven battles?
You cannot go beyond the seventh battle.
The maximum you challenge each time is seven.
Let me explain this :
For example you finish the seventh battle the first time, so your highest record will be 7. So if you challenge two times without losing your highest record will be 14.
At the seventh match of the third challenge (you didn't lose until the seventh battle of the third match) you will be required to battle the frontier brain (Barry's Father).