My guess is that this happens because of max HP being rounded to nearest 5 and current HP being calculated as a precentage of max HP which leads to inconsistency if the changed consitution value swaps between up- and downrounding of max HP. In any case it's pretty irrelevant as the HP loss is minimal, especially if regenerating (above 85% max HP) and there is no reason to stand around switching equpment just for the sake of it.
If you really need a rationalisation for it, roleplay it as an alergic skin reaction to pig skin constantly rubbing against your feet. :p
