Is there a leak? Does the pressure build up enough to shut it off? Is the new one wired in correctly.
If it is wired right, and the pressure builds up, and it is set to a proper pressure, and it operates, it must shut it off.
A leak, keeping the pressure down, or wrong wiring (for a new assumed functional switch) would be the only thing keeping it from shutting down.
The moral of this laundry list is, you should post everything you see about the problem.