It depends on where you live but most likely they cannot deny your winnings as you did not cheat, however bookmakers especially local ones are going to notice really quickly that you are winning money and that you are in fact choosing the best lines over and over again so eventually you will be banned to gamble there, this is why when it comes to arbitraging opportunities it is better to take your activities online as there are thousands of casinos that you can use if you happen to be limited or banned in one of them.
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.
It is known that arbitrage bettors do something like this in order to keep betting in the same casino, but as I have said with so many casinos online for the most part there is no need to do this as you will always have a new casino you can try and get some arbitrage opportunities out of them, besides there is the possibly that such practice is forbidden in the terms of the casinos, and if it is, at that point they could actually ban you and confiscate your winnings as you are not following their rules.