Shallow well pressure problem

My problem is similar to others I have been reading about here, but not exactly, so hopefully I can get some good advice.
I have a shallow well jet pump, a Gould with a attached pressure tank. Came as one assembly. It was installed five years ago and has been fine until now. Static pressure is a bit above 40 psi, when I use water I get good pressure for a few minutes then it starts dropping off. Water still flows but the volume and pressure fall off until the flow is very much reduced and pressure is near zero. The pump is still pumping and will stay on as long as I am calling for water. When I shut off demand, the pressure builds back up to 40ish and shuts off. I cannot see any leaks anywhere. Pressure stays up as long as I leave all the faucets closed. Hot and cold are the same.
Ideas and suggestions ?

If you still have at least 20 PSI on the inlet side from the city, the pump is just not working properly. It maybe just a clogged jet nozzle.

Thanks, I will look into that. But, not sure what you mean by "inlet side from the city". I have a shallow well.

Oh I thought you had 40 PSI static from city pressure to boost. With a shallow well at 40 PSI, you probably have a leak in the suction pipe somewhere.

I don't know where you are, but if you are in an area where wells have a screen, your's may be getting plugged. I used to change up to 4 screens a day back in the 60's - 70's.

We are in a very sandy area of NW Wisconsin just south of Duluth MN. The well is a driven shallow one pipe type. Frankly I do not know what type of tip is on the pipe. Screen or ?? Assuming that is the screen you mean. I do not see any easy way of changing that. And I do know know of any other screen other than my whole house filter which is new.
Sorry to be a knob...

I was in Michigan and most wells there were screened, same for Wisconsin. If it's a driven well like you say, you can either pull it out and replace the screen or try to find some Nu-Well tablets and use them to clean it.

Thought this might be of use to others so here is what we did. I had the existing well inspected by a local person known to be trustworthy. As it turns out, the well does not meet code and should be replaced. Code problems were to close to the house overhang, in a pit and not deep enough. So we bit the bullet and had a new well put it. We would have to do if we ever wanted sell anyway. Our pump was fine. Now we have excellent pressure, great water (was tested). Now I need to figure out how to keep it from freezing, but that's another subject.

What do you mean "keep from freezing"? Since a pit is not up to code, didn't the installer put in a pitless adapter? That is what keeps the lines from freezing without a pit.

No, a pitiless adapter would not work in my case. Because of how the water enters the house and the location of the underground power line.

In Wisconsin, Pitless Adaptors are required by the Health Department. If you had a new well installed without one, it's not code. Your local person may not be as trustworthy as you thought.

That is not true, I have all the code documents and mine is like fig 6 attached. No pitless adapter is required.

In that case you do have a freeze problem until you figure out how to keep it warm.