You are right, if you don't play carefully you can never save your deposit and if you leave it on the casino site you will fall into the trap of fraud later. When you gamble with your real money the most important thing is that you can be sure and secure that your transaction is safe and that you get your winnings without any delay and quickly. Good online casinos care about these things and strive to provide the highest and best service possible. gambling sites should be analyzed to choose the right casino.
No matter how good or trusted the site is, the end responsibility remains on the user to keep his funds save and not to over trade. Being a responsible gambler is more in favor of the gambler and not for the gambling casino because they wants that people wager more and therefore more chances of losing the money.
Coming to the OP topic, if anyone is playing at stake or any trusted gambling site, he will not shift to any other site unless he thinks that the service quality of that site has deteriorated or he is having any other issue. Usually, people will never leave a good gambling site that is providing good services and fulfils the gambler's needs.