Brake dropping when pressed

When I press on the brakes to slow down, keeping the same amount of pressure, it would randomly drop about half an inch and causes the brakes to grab harder. I also noticed it dropping when it is being pressed during idle and im not sure whats causing this. I've never had this happen in any other cars.

I've tested the brakes while the car is off and there is no loss in pressure. Also had the brake fluid changed about 2 years ago when I first got the car (used) and noticed the problem.

Another problem I've been having is the brakes squealing when I apply light pressure. It goes away when I press harder on the brakes. At first the mechanic said my front pads were worn out so I had it changed and the sound went away for about a week and then it returned. Then I changed the rear drum brake shoes and the same thing happened. Not sure if this is related to the brake dropping.