I have had a knock off of a Stanley 78 for years now.  Although I haven’t used it often, I am getting into more hand work, and want to use it to cut rabbets.  The problem I am running into is the rabbets are not square along the side (with grain cuts).  It seems that with each pass, the plane moves a small amount away from the one previous, so the rabbet ends up with a ledge in the inside corner of the cut.  While planing I am making sure I keep the plane level, and put lots of pressure on the left side to try to keep it against the shoulder.  But for some reason, it always seems to step away from the shoulder as the cut goes deeper. 

Am I doing something wrong, or is there a set up issue with the plane?  I have tried two different blades, but get the same results.  Anyone have any ideas?

Thanks