Why does my pump loose pressure

There will be water come out of the heads for a few min after they shut off to bleed the pressure off there is no way to stop it you might turn your system timer down a little

Sounds like the check valve is leaking. It's in the water line between the pump and the pressure switch

There must be a hairline crack to where it is only noticeable when the pump starts to run creating a vacuum.

If in the past your system can build-up pressure up to 40 psi even if the supply valve is open and water is being used in your house, then your pump impeller maybe already worn out that's why its pumping capacity was reduced.

Sounds like a pump. You should have 43 lbs of pressure after system is primed by turning key to ON. Pump will run for 5 seconds and shut off if engine is not running. It should hold pressure for 30 minutes with just a few lbs drop. If not, it is the check valve, internal to the pump or the fuel pressure regualtor on the fuel rail. Hardly ever the latter

When a pump goes on and off there is a water leak somewhere.
There should be a gauge. Let the pump build up pressure and watch the gauge.
The pressure will probably be dropping. This means that water is going somewhere. The leak could be anywhere that you use water, sprinklers, sinks, hose lines. If there is a valve above or near the pump, shut that valve and see if the pressure stops dropping. If the pressure stays up and the pump stops cycling on and off, the leak in in the pressure piping somewhere, you must locate it and repair it.
If the pressure continues to drop even with the discharge valve shut, the water must be leaking back into the well. There is a check valve somewhere on your line between the well and the pump. If this check valve is leaking, pressure will drop and the pump will come on to restore it.

If it is possible to shut off the discharge of the pump, shut that valve and watch the pressure gauge to see if it is dropping.

The pump is putting out too much water for the sprinkler.
You can raise the pump shut off pressure at the switch until it is higher than the pressure that the pump runs at with the sprinkler operating. You should have a surge tank connected to the system to give the pump time to balance with the sprinkler.
You can use more water with the sprinkler. This could mean adding another sprinkler or increasing the nozzle size of the existing sprinkler.

Your loosing your fuel pressure in the system when you shut down the engine. You could have a leak in your fuel pressure regulator or your return fuel line check valve is worn, which is located on your fuel pump sending unit housing. The other thing also is you could have a weak fuel pump so check your fuel pressure at the shredder valve, you should have 62-65 PSI when the fuel system is pressurized (engine not running). Causes for weak fuel pump, bad ground wire from pump to frame or worn out pump and a dirty fuel filter.
Check your fuel pressure to ensure you have 62-65 PSI and check to see how fast your pressure will drop, a fast drop will indicate a leak in your system as to the fuel pressure regulator or check valve at the sending unit.
Thank you for using Fixya and good luck

yes,

SOUNDS LIKE YOU HAVE A LEAK DOWNSTREAM PROBABLY UNDERGROUND. THE PUMP HAS NO REASON TO COME ON EXCEPT TO BUILD THE PRESSURE BACK UP. HOPEFULLY YOU HAVE A GAUGE IN THE DISCHARGE LINE YOU CAN WATCH IT DROP AFTER THE SYSTEM SHUTS OFF. HOPE THIS HELPS, JODY