Pressure switch always runs pump at 15 psi doesn't cut out

There is only one adjustment screw because it has a fixed differential. A 20 lb differential is standard. I recommend a 40-60 pressure setting which gives you an average water press of 500 psi. With a 40 cut-in, your tank pressure should be set at 38 psi. There is a schrader valve at the top of the tank. Use a tire gauge to set it at 38 psi. Do that first. Now set your press switch by running water and observing at what pressure the pump kicks in at. Don't worry about the cut-out pressure. It's trial and error.
Let the pressure build up above 45 psi and then run water until you hear the pump kick on. Keep doing this until the pump kicks on at 40 psi. It may take a few tries, so I recommend having someone else turning the water on and off for you.

The 34 psi of the pressure tank sounds high, but it depends on what the cut-in pressure is set at in the pump pressure switch. Typically the pressure switch is for 20-40 psi or 30-50 psi. To establish what the pre-charge of tank should be , you need to establish what the pressure switch setting are (i.e 20 - 40 psi , etc.) Run the water and watch the pressure gauge and note at what pressure the pump comes on. The pressure tank needs to be pre charged 2 -4 psi below that cut-in pressure. So if the cut-in pressure is say 30 psi, then the tank needs to be pre charged to 28 psi.
To pre charge the pressure tank, turn the pump off. Drain the pressure tank of water to relieve all pressure in the tank. Then check the pressure of the tank at the air valve. Set the pressure to 2 psi below what the cut-in pressure is.
If you adjust the pressure switch, say from 20-40 to 30-50, you will need to go through the procedure of re adjusting the pressure in the tank. I hope this helps....

The water pressure is adjusted with the pressure switch, which turns the pump on and off. The pressure switch is typically set for a cut-in and cut-out pressure of 20-40 psi, or 30-50 psi. Usually there are adjustment directions on the inside of the switch cover. But, there are several other factors that may affect the house pressure. If there is a pressure tank that is pre-charged, the tank pressure may need to be reset, or the tank bladder may be ruptured. Have the entire system checked out.

If you have a bladder - type water pressure tank, it probably needs to be purged of air and then pre-charged to 18 psi. There may be directions on the side of the tank. Turn the water Pump off. Drain the tank of water. Check the pressure of the tank at the air valve on top of the tank. The pre-charged pressure of the bladder is set to 2 psi below the lower pressure set by the pressure switch, so in your case, the low end pressure is 20 psi. Therefore, the pre-charge pressure of the tank is 18 psi. If you set the pressure switch to operate at 30 -50 psi, then the pre-charge pressure would be 28psi., etc. Once the pre-charge pressure is set, turn the pump back on. ( don't forget to close the drain valve). The system should cycle normally. A tire gauge works to check the tank pressure. An air compressor may be used to charge the tank, but be careful not to over- inflate the bladder. A tire air pump may also be used. Hope this helps....

If you have a pressure tank, make sure that 1/3 of the tank is full of air...this may solve your problem
Or maybe you have to install a "foot valve" on the suction of the pump to solve the problem

If it's pumping up to 135 psi, shutting off and then restarts at the same pressure point since it was new, the pressure switch may have been set low at the factory. I don't know which model you have but most pressure switches have directions inside their cover as to how to adjust the cut-out and cut-in pressures. Be careful doing this, overpressuring the tank is dangerous. There is an adjustment screw or bolt that changes the pressure on the switch spring. Some pressure switches have two screws, one for cut-in and one for cut-out pressure. A few have one that adjust both pressures. If you do adjust the cut-in/cut-out levels, do it slowly and cycle the motor a couple times between each adjustment to see where it turns off and on. If the compressor is doing what you want it to, only pumping to 135 psi, it will live longer than if you adjust it up to 150 psi. Those last 15 psi of air are hard to get and will mean the motor will be running longer and more heat will be building up in the head.

Your concern is very well placed, at pressures that high a lot of damage can be caused by a failure. According to the manual for this model air compressor the approximate cut-in pressure is 160 psi and the approximate cut-out pressure is 200 psi. Meaning it should pump up to 'about' 200 psi and shut off and not come on again until it gets down to 'about' 160 psi. They say approximate and I say about because it's not an exact science setting the pressure switch. Spring rates are not always exact, pressure guages are not that precise, etc. When turned on, it should shut off at 200 psi +/- 10 lbs. If it goes more than 10 lbs over that (220psi), I'd recommend you get the pressure switch and or guages checked or replaced.

You probably have a bad pressure tank. The pressure tank bladder can develope a leak internally nad become saturated with water which won't allow it to provide cushion for the pump to gain and maintain pressure. It could also be that there is little or no pressure in the tank. Check your pressure and add to at least 40 psi. If this helps , but doesn't totally cure your problem, you have a bad tank.It could also possibly be a bad check valve but, you would probably lose all of your prime.

Have you checked to ensure that there are no leaks from your hose or any of the connections?

You have a defective pressure switch.But replacing the switch. Do the following; Open the pressure switch cover, and find the two adjusting nuts. One is for the cut-off pressure (40psi) and the other is for the cut-in pressure (20 psi). Adjust the the nut with a longer stem counter clockwise (loose) with the pump running. Take care not to touch the power line attach
to it. Continue the adjustment until the pump stops,
at 40 psi. Then, observe - Pump must stop once the
pressure is attained. Then, open the valve until it
start (20psi).. Then you can adjust the other nut to
cut in at 20 psi.
To prime the pump; open and fill the priming port full
with water.and replace the priming port plug. Set
the water flow control valve at full close position.
Switch the power on to run the pump and slowly
open the control valve to appropriate setting such
that the pump doesn't lost the suction. Send your e-
mail for further comment. God bless u