First thing to check is the fluid in your Power Steering pump. If the fluid level gets low, your pump will squeal or quit working altogether. Once the pump gets overheated (due to low oil level) it will most likely need to be repaired or replaced depending on the vehicle. There are several variables to consider such as serpentine belt, rack-and-pinion or steering box condition, but the first thing mentioned is where you should start.
If you cut the engine, you will lose power steering.
No.
Its has HydraBoost Braked, operates off the power steering pump.
When the engine stalls you lose the power assist.
probably going to lose your steering
power steering pump
Yes, you can expect a car that has a serpentine belt to lose power steering when the belt breaks because the belt goes around the power steering pump's pulley.
Have had the same problem in the mornings or when the engine is cold. I suspect the power steering belt is slipping.
power steering pump or pully may be bad causeing more stress on the belt witch strains the motor an makes it lose power
There are 3 things that can happen when you lose power steering. #1 there is not enough power steering fluid, there might be a leek in the system. #2 The belt that connects to the power steering pump has come off. #3 The beerings in the power steering system has seized, usually only happens if the car is very old.
Power steering like all other accessories tax the 'power' of the engine; if there is a problem in the power steering causing excessive load on the engine it will loose power (more so in low horsepower engines).
Your Suburban likely has hydro-boost power brakes which are hydraulically powered by the power steering pump. If you lose assist to one, the other loses as well.