The only reasonable effect that a magnet could have on a compass is to strengthen the magnetization of the compass making it respond more strongly - faster. This will not deminish the accuracy at all. Only if you were to force the needle of the compass out of alignment with the magnet and then move it about as was suggested in another post. Fortunately for you compass the needle will align itself with the magnet so it can only be strengthened. Further the needle is a permanent magnet as, presumably, is this other hypothetical magnet. Permanent is permanent. The only things that scatter the magnetic alignment of a permanent magnet are things that will disrupt the crystaline alignment of the metal itself - Extreme heat or impact. in the presence of these influences it is possible to reverse the magnetic alignment of the magnet or eliminate it. completely. But then again yyou are not likely to be throwing you PSK in the fire and then expecting it to continue to be useful are you.