It's not a free pass going to higher pressure.
First off, any given pressure tank has a larger drawdown (tidal volume, amount of useful water stored) at 20/40 than any higher setting. Unless you increase the size of, or add additional pressure tanks, at a higher pressure your pump will stop and start more frequently (which is usually considered to be a large factor in how fast it wears out - running longer and starting less is better than running less each time, but starting more.) As you can see from the example chart below, for a given tank, 40/60 is already less than half the volume stored at 20/40.
This version is not quite as bad (they do vary a bit):
You will need to check your tank, but most pressure tanks are good to 100 or 125 PSI (the ones in the upper chart are only 75 though), so that's probably not the limiting factor. You'll need to check what the pressure on your hot water heater's temperature-pressure valve is, but it's probably also fine. My pump supplier suggested (and I installed) a 100PSI overpressure valve on the system as the pipe entered the house.
Many common items (toilet valves, etc) don't really like pressure over 80 PSI (yes, I know you only proposed 70.) 60/80 is about as high as you can expect to adjust most pump control valves to.
It's not the most common situation, but if your well pump is marginal for the depth you may reach a situation where it's cannot reach the higher setpoint as you use water and draw the well level down - so it will sit and spin but not reach the shutoff pressure.
If your system was designed for 20/40, I'd suggest doubling or tripling your tank capacity if going to 40/60, and tripling if going to 50/70. How important that is may be influenced by how deep and inconvenient and expensive your pump will be to change when its time comes. Cheap and easy, maybe you don't bother increasing the tank at all. Expensive and a major hassle - you might consider more tankage a good investment.
Allowing for the possibility that it could be otherwise as diagnosis via internet is imperfect....
I see both a pump problem and a check valve problem here. While they may be located in the same place (if your only check valve is on the pump - which is the way mine is set up) they are not the same thing...though I also see another possibility that would do both.
- Pump problem - pressure not getting above 27 PSI, or 15 with a faucet open.
- Check valve problem - when you shut off the pump the pressure drops
to zero - unless you are using water, the pressure should stay at 27 if it was pumped up to 27. When you only had 10 PSI in the tank, there should have been some water storage - when raised to 38, no water could possibly make it into the tank, since that's designed for 40/60 PSI operation and won't take any water until the the water is over 38 PSI.
The third possibility - you have a leak in the pipe above the pump and check valve - so the pressure is limited, and the water drains away from the leak without the check valve being to blame. If you can go and listen at the top of the well while someone else turns the pump on, you might actually hear this leak, if its in the well above waterline. Or you might have a recently soggy spot in the yard if it's after the pipe leaves the well.
While I don't think it's to blame in this problem, I'd also suggest rechecking your tank pre-charge to see if it has stayed at 38 PSI or started to fall again. Often when the precharge becomes low it's not simply a matter of needing to add air - it's a failure in the bladder or diaphragm.
Best Answer
If the pressure is going down, you're losing water somewhere.
If you have a main shut-off valve on your tank (usually between tank and rest of house) shut that:
Alternatives to a main shut-off valve are certain types of bypass valves on softeners, carbon or iron filters (the type with two valves to turn -- if you just turn one, it shuts off the water), or cartridge filters are often installed with shut-offs so you can service them.
Diagnosing interior leak
Unless you can isolate the problem to your well, go around your whole house and shut all valves (including toilets and outside taps) and inspect for any leaks.
The time of year is also a hint that you might have had a frozen pipe that burst, and has now melted and is now leaking, so you should definitely take a close look at areas near pipes on/near exterior walls and at any outside hose bibs.
Diagnosing leak in well
Almost certainly this will involve pulling the pump/foot valve out of the well. You'll have to turn off the pump and drain the pressure first.
Before you pull it, see if you can spot an obvious leak above the water line (eg, at the pitless adapter at the top). Pro tip: use a good spot-type flashlight or a mirror to reflect sunlight so you can see down.
Once you pull the pump out, inspect all the fittings for any signs of damage. By far the most common problem is the check valve at the top of the submersible pump sticking open (either spring or other parts corroded, or something actually lodged in it holding it open).
If you still haven't found anything, this starts pointing at a leak in the line going to the house, which is significantly harder to deal with (involves digging), and in worst case, involves digging the entire line up. In my experience, this will usually be: