winter thaw or not, its still water & rain'll also seep down & leak in the same weak spot,,, think of your very fine bsmt as a ship's hull below waterline & it becomes more clear,,, its always better to prevent wtr from entering than managing once its inside,,, how far below exterior grade is it showing up inside ? thyen again, it it can't enter where it is not finding an opening, it will show up somewhere else,,, proper grading & gutter discharge are the 1st things to ck.
usually ' seeping up ' = wtr seeking its own level altho it could be hydrostatic pressure,,, ' about 4' thick ' isn't much data nor is ' as well as the two stairs ' - more ideas to follow as more inf is post'd , , , , ,