I had this very same problem. The vacuum booster in my car tested just fine in that I had no vacuum leaks and could measure ample vacuum with a gauge.
The problem was that the piston that pushes from the vacuum booster into the master cylinder was adjusted too far out. That is, the overall piston length was too long. If this happens, the piston always maintains pressure on the master cylinder with too little reserve at rest. You can think of it as a sort of unwanted pre-charge. When the the pedal is pushed halfway and there's no force left on the brakes it's because there was too little fluid to push.
Why? Unless the piston could recess far enough back into the booster at rest, the master cylinder could never draw in as much fluid as it needed from the reservoir. It's always deficient. Hopefully your vacuum booster has an adjustable piston. Use a caliper to measure the depth of the master cylinder bore. It should be about an inch, but you need an accurate measure. Then adjust the vacuum booster piston to (probably shorten) the same length, minus maybe another 1/8" or 3/16" for free play. You need to make sure that at rest, there is no pressure at all on the master cylinder. But you also don't want slop because you'll lose pedal travel. That might take a little trial and error.
When I performed this operation it solved the problem perfectly. To be honest, I never really thought much about this adjustment until it was too late.
One other thing: as long as you're in there, make sure your vacuum booster check valve is working.
-marcus
