Well systems can get complicated. And you cannot just start adjusting things. This may be beyond your ability to diagnose. Do you understand how the system works and the relationship between the pressure tank and the pressure switch? Do you know the HP of your pump? Do you know how deep the well is? Is this a submersible or a jet pump?
You need to make sure that your pump can handle pumping to a higher pressure before you make any adjustments. The pressure in the tank needs to be adjusted also. You could have a faulty pressure switch or the nipple to the switch could be clogged. Have you observed the pressure on the gauge when this happens? Can you hear the contacts on the switch closing, but not producing water? Does anything get hot? Boy, there is just so much to all this and there is tons and tons that I don't know.