The first thing to check is the mastic or sealant around the door frame. Even the smallest gap will allow water ingress; I used 5 or 6 applications of Sikaflex sealant built up in layers to make sure there was a good seal. If the wall is of solid construction water can soak straight through the stone/brickwork, especially through the mortar. With a cavity wall, water pools up on the part of the doorstep behind the frame, soaking through the mortar on the lower brick course. There may also be rubble etc piling up on that bit of the step, which will assist water migration, and hinder drying - ditto for anything bridging the cavity at whatever height. This may have been going on for years before it becomes obvious, so if you have wooden floors, I would recommend checking on the floorboards and joists underneath if possible.