After replacing the drop targets with the stern sent kit I still had the same issue as before. The first drop target would not stay up during reset around half the times.
I finally took the assembly out again and did something different this time as I noticed that the design decision has the coil mounted on the back side near the 3rd drop target. Being on one side and not in the middle, the arm pulled by the solenoid would basically never be straight when pushing the targets up. This would in turn allow the drop targets to move not completely in parallel but have them reach the top with the target closest to the coil first.
So I needed to give the 1st drop target a bit more push upwards for it to stay up.
I looked at the coil assembly and noticed that the curved disc spring washer was placed in a way that would distance the coil far enough to reduce the arm movement. I repositioned the washer on the back side and tested the drop targets again.
I had not one fail in around 20 plays.
So it seemed to have been fixed for the time being.
I wonder if this washer was supposed to be there in the first place or I just found a hack good enough to fix a bad design decision?