When the pump fails altogether, you'll have zero steering assist. A power steering pump that's leaking will cause the fluid to deplete faster, resulting in noise and, eventually, a loss of steering assist. Power steering fluid will deplete faster if the power steering pump is leaking.
before the power steering is not working as it should be when the pump stops working, in that case the answer is immediately. The pump supplies pressure to assist the driver to turn the steering wheel and if the pump stops working the effect will be felt almost immediately, the steering will however still work but the driver will need to put in some effort to turn the wheel.
A whining noise while turning the wheel of your vehicle indicates something wrong with your power steering system. It could be a leak in the power steering pump or the fluid level could be low. If the power steering fluid level remains this way for too long it can damage the whole power steering system.
Most modern cars come equipped with power steering, but as systems age they can wear out. Problems with alignment or the power steering pump can also cause the power steering system to stop working. Check the power steering fluid level. If there's not enough fluid, it'll be hard to make turns.