If the lever you are referring to is on the side of your pressure switch:
![Pressure switch with low-pressure cut-off](https://i.stack.imgur.com/xDSOC.jpg)
Then I unfortunately have not very good news for you. As the name implies, this cuts off the switch entirely when the pressure drops to about 10psi below the cut-in point (eg, most well pumps are set up to turn on at 40 and off at 60psi, so the low-pressure point is about 30psi). It's there to prevent the pump from running dry.
Potential cause: low-yield well
Without any other information, my best guess would be your well is not producing enough water to keep up with demand. This seems to be consistent with your statement that it only happens after 30-45 minutes: there is enough reserve capacity in the well itself to supply you for a while, but ultimately, the rate of water entering the well is lower than the rate you're using water.
The ultimate fix for this is to install a cistern or holding tank that the well pump supplies, and have a second pump in that that actually supplies the house. The cistern is controlled via float (instead of pressure switch) and the well pump is protected by a load-monitoring device (eg: Pumptec by Franklin-Electric) that turns off the pump electronically if it senses no-load. The size of the tank largely depends on how much capacity you want, what the actual yield of the well is, and logically where the tank will go and how big you can fit. Commonly, the cistern is a large cylindrical PVC tank installed in the basement.
Potential cause: undersized pump
The other main cause would be an undersized or under-performing pump that is unable to keep up with demand. The symptom of this would be that the pump runs constantly during use, rather than cycling on and off, and that you generally have a consistently low pressure for that time prior to the low-pressure switch cutting out.
Replacing the pump in this case may help, but if you have a low-yield well then it's a waste of money. Considering it's been happening for 14 years, it seems unlikely this would be something mechanically wrong (I'd expect the condition to worsen over time, or for the pump to have failed by now) and more likely that the pump was undersized, IF you also have the symptoms I described.
What next?
If you can determine the pump is undersized, then replacing it with a larger pump would be one way to remedy the problem (assuming there is no yield problem also).
The next best course of action would probably be be to test the yield of the well. You may be able to do this yourself, but a professional will bring in a much larger pump and test the flow right at the well, bypassing all the pressure controls and inside piping that would interfere with the results.
Of course, seeing as you're selling the house, you'll have to make your on judgement call on what you do or disclose -- advice on that is beyond the scope of this site.
My recommendation is to build a "float pan" under the run of Cu pipe in question. As Ed Beal suggested, don't depend on the sump pump as a diagnostic tool. The pan only needs to be an inch or so deep, as you expect it to be bone-dry all the time. Put a float valve on the pan, and tie into well pump power as planned.
BTW, I didn't come up with this on my own: central air conditioners' air exchange handlers have this sort of arrangement, to avoid disaster if the drain line clogs.
Best Answer
Simplest solution from scratch: - put the deep well pump on a timer that only lets it run for a short length of time when filling the cistern. Say 15 minutes every hour, or whatever ratio actually works with the pumping rate and refill rate. So you'd have a (float switch?) calling for water into the cistern, and you'd have the deep well pump set to pump for 15 minutes (or whatever time works) and be off for 45 minutes (or whatever time works) when the cistern is calling for water.
You can try restricting the flow from the pump (which will, counterintuitively to most, reduce its power draw) but this will result in high pressures in the piping from the pump to the restriction - possibly higher than is advisable, depending on the pipe and fittings.
Simplest solution if the parts are already in place: If the deep well pump was set up with a normal pressure switch and bladder/pressure tank, you could also simply use that arrangement as the source of a restricted fill to the cistern, and the pressure switch would act as the "timer" and the restrictor valve would act as the restriction, without any excessively high pressures. The cistern float switch (or the float itself, mechanically) would control a valve in line with the restrictor valve. Set the restrictor valve for a flow slightly lower than the well refill rate.
Well--Pump--Pressure switch--bladder tank--restrictor valve--float-controlled valve
If your pressure switch has a low-pressure cut-out it will shut itself off (until you reset it) if the water level gets too low in the well. In that case, you could close the restrictor valve some to reduce the flow before restarting the pump, as you'd know the pumping rate was exceeding the refill rate.
You do not mention but presumably must have either an additional pump on the cistern, or you have located the cistern sufficiently far above your dwelling to provide gravity flow from the cistern; but that does not materially impact this question.