How far is the pump, as measure along the wire, from the breaker panel? I doubt that the wire is the problem.
Check the voltage at the switch to make sure you have 230 Volts when the pump is running. If you have at least 220 Volts when it is running then you don't have a wire problem.
What are the make and model of the pump? I can't imagine a properly sized 1/2 HP well pump that wouldn't deliver the pressure from a system to a tank.
One problem you might have is if you got a high-head pump and are operating it against low pressure. You could be overloading the pump which could cause the internal overload protector in the motor to open. When that happens a pressure switch with low-pressure-cutoff would cause the switch to open and it would not restart. You can check that by turning off water usage and seeing if the pump stops (no increase in pressure) while the pressure switch contacts remain closed.
If you got a pump that is not matched to the pressure of your system you might have to put a valve in the line to throttle the flow.