1996 Chevrolet Tahoe Brakes

Some GM boosters have two diaphragms and a problem with one will cause what you described. That shouldn't happen though just from hard braking unless the vehicle stopped really quickly. There is a valve that falls out of position. You have to worry about that valve if you get a used booster from a salvage yard. Always carry it and haul it in its normally-installed orientation. If you set it on its front or back, that valve can fall out of place and you'll have the same problem. A rebuilt booster will come with a plastic cone inserted to hold that valve in place during transport. The clinker to this problem is the only people who even notice there's a problem are those who have owned the vehicle for a while and know what normal feels like. To other people unfamiliar with the vehicle, the brakes seem fine.

The valve I was referring to is inside the booster, not the vacuum check valve. That vacuum check valve can cause what you're describing too, but there will be other symptoms with it. One is you'll have normal power assist while the engine is running or decelerating during coasting, but even a slight acceleration will lower vacuum enough that you won't have much assist. That valve is supposed to store enough vacuum in the booster for two or three power-assisted stops during periods of low vacuum, like when accelerating. To test that valve, you have to start with normal power assist, stop the engine, wait perhaps ten to twenty seconds, then apply the brakes. You should still have power assist for at least two pedal applications. If the check valve is leaking, you will have no power assist as soon as the engine stops.