The bulb will not remain hard or even firm but if it is obviously being "deflated" you either have a restriction between it and the tank, (strainer in tank blocked maybe) or the tank is not venting ( try with the cap off)
The primer bulb should not stay hard when the engine runs, but it should not collapse. If it collapses there is a problem with the bulb, or something between the bulb and the fuel supply, unless the tank vent is closed or blocked.
Be sure that the arrow on the primer bulb is pointing towards the engine.
