SGPro does not anlyze previous frames in order to determine what to do next, but the AF routine does have a notion of "runaway focus" using ((2 * data points) + 1).
In order for us to better analyze what is happening to you, we would need logs showing the AF run and a full AFPack.
Possibly, but maybe not. If the stars were rejected due to size (too big or too small), you have some control over this. If the stars were rejected because the flux signal did not deviate from background sufficiently, then no, we don't offer control over that.