<<That sounds like a vacuum problem, i.e. the vacuum in the reservoir
down" after the engine is shut off. I had the same problem and was able to
fix it by replacing the vacuum check valve attached to the brake booster. However, there are many hoses ultimately attached to the vacuum reservoir, so it can be a hose has fallen off, or a broken connection somewhere>>
A quick way to check the integrity of the vacuum system is to set the A/C to air conditioning mode. Go up a hill and go to full throttle - doesn't matter the rpm and it doesn't hurt it to ride the brakes a touch to hold the speed down. The A/C should remain working. If it goes to the heater mode in less than many seconds there is a leak. Then all you have to do is find it.