Booster failures are quite rare (but possible). You might try disconnecting the vacuum to the booster and then drive the car (with the caution that you will need to press HARD on the brakes to stop) and see if the problem persists. If it does, then it's NOT likely to be the booster.

Sometimes the seal from the master cylinder to the booster lets go and the booster fills with fluid. This can impare function, but I don't know if the symptoms match what you have described.

Marshall