The Sturmey8 will only slip into 1st if the shifter cable is mis-adjusted. The issue is that it is very easy to be slightly off, as the Sturmey8 is EXTREMELY SENSITIVE to being just right. It doesn't help that the markings on the hub that are supposed to correspond to proper adjustment don't actually correspond to proper adjustment, but are only in the ballpark.

Once you actually have the adjustment dialed in, mark the position yourself so that you can get it again in the future.

Folding and unfolding should not affect your adjustment, provided that the nut on the cable is tight, and cable routing is properly designed on the frame.