It sounds to me like your bladder tank is either shot, or needs some air (assuming you system has a bladder tank - if not, you could still have a tank problem, but the fix is different). Another possibility is that the pressure switch is faulty. Your pressure switch normally has about a 20# difference between on/off. Then, based on the size of the bladder tank and the recovery rate of the well, you'll be starting from somewhere between those two pressures, as you use water, it will drop to the minimum setting, the pump will come on, and as long as it can maintain the flow rate, typically will gradually build back up to or close to the max. If your flow is greater than the pump's ability to match your use, it will drop. So, it could also be your well or pump aren't producing. this should become fairly obvious if you can watch the pressure gauges.
First thing I'd do is check and adjust the bladder tank air pressure. To do this, shut off the pump. Open a valve somewhere until the water stops flowing. Then, using a tire pressure gauge, check the air pressure on the tank. It's probably low, or non-existent. It should be 1-2# below the low-pressure turn on point of the pump's pressure control switch. Pump it up to there. Let it sit for awhile, then check it again to see if the bladder is leaking. If it's okay, close any open valves, then turn the pump back on and see how things work.