Most books dont have a specific number. It depends on alot of factors. What sport you are betting, what plays you are betting, and how long you have been consistently winning are the three most important factors.
If you've had alot of success betting NBA playoffs or another "major" sport, I highly doubt they will cut you off. If you've been tattooing them in handball, challenger tennis, small time soccer leagues, or another relatively obscure sport. Expect to be cut off sooner than later.