Just because minimum wages go up, doesn't mean humans are getting replaced. Instead, people often adjust their price limits (e.g. if cleaning was thought to generate $10, and then you don't clean for a while, you'll feel it warrants $11) and workers get better pay. The workers who do get fired due to financial constraints can now get a job elsewhere for more money.
I agree that there is a breaking point and that point does vary by company, but that breaking point (for the vast majority of things) happens to be far greater than zero