Sounds like the house I grew up in, the pressure tank would leak air, we'd have to recharge it every 6 months or so.
The whole point of the air in the tank is to provide a pressure buffer. Without the air, the instant the water is turned on at a faucet, the pressure drops enough to kick on the pump, the pump will instantly overcome the cutoff point (because the pump generally has a higher capacity than the flow out of the faucet). As long as there is any demand on the system, the pump kicks on and off every few seconds. This can burn out or overheat the motor quickly.
To address your question about the pump never reaching the 4 bar pressure, as others have said, if it's a 3 phase supply, switch any two leads, and see if that helps.