Based on the pressure cycling, I assumed I drove the well point partially through the water bearing layer (I don't know how thick the aquifer is). So I removed a 2 foot section of vertical pipe, in turn raising the well point 2 feet. Hoping that this would put the well screen completely in the aquifer.

I then ran sprinklers non stop for 5 hours with no pressure drop and came to the conclusion that I fixed the problem. However, a few days later i was having the same problem.

I'm getting about 5gpm at 30psi.
My setup is as follows: (see picture)
A stainless steel well point/screen 1 1/4"x4' with the top of the screen 2' below static water level. No casing. The well point is plumbed to a Goulds J10S 1hp jet pump with 1 1/4" galv pipe and drive couplings with a check valve about 5" from the pump.
I have a 4.5 gallon goulds hydropro pressure tank (set 2psi below the pump cut in pressure) on top of the pump.
After the tank I ran 1" pvc to two sillcocks outside the house.

A few things I can think of causing my pressure fluctuation.
1. Well point is driven through water bearing layer and sucking air from below.
2. Water level is drawing down around well point and sucking air from above.
3. 1 1/4" x 4' well point does not allow enough water to pass through (not likely because I had 5 hrs of continuous 30psi).

Do I put in another well point and connect the two with a manifold?

I don't know what to try next. Please help.