It's not that hard to prevent yourself from getting banned when you are winning, you can always use other people to bet for you. I think sports bookies would not banned you if you they getting equal action and they remain profitable, it's just normal that some are winning and some are losing, what's important is their operation is profitable.
In theory, this is easy, but in fact, using other people for this is almost unrealistic - identity checks are carried out at all stages of the cash flow - at bookmakers, in the payment system, at the bank. There are too many risks to trust someone with your money. The only option that is more or less normal is the help of relatives.