The really big bookmakers have a lot of customers. I don't think they are easily steered by the fact that they have a problem with a customer. After all, every bookmaker or casino has a problem with a customer, often related to payout of course. But it's true, a reputation can be destroyed in moments.
If they can't solve the issue then they will surely break their reputation and soon will be bankrupt and when their customers request for a payout so they can't pay them. If the customer having requested for a payout and have a problem then that person will raise a scam accusations and their reputation will also change so I would say that reputation will break easily if they don't something about it and their platform may shutdown.