To answer this question we should turn to the oracle:
The relevant quote is:
"Nothing affects a cookie's texture more than the melting characteristics of its fat. Butter has a sharp melting point meaning that, uh, just a few degrees difference between a solid and liquid states. So since conversion occurs at a relatively low temperature, the resulting batter spreads prior to setting."
The problem is that shortening melts at a higher temperature than butter and so cookies made with shortening typically rise more than butter made cookies. Thus your rising problems are probably not caused by the type of fat.
I suspect that the temperature of your fat might be causing the problem. If your butter came from the fridge and the shortening was room temperature then the shortening cookies would melt faster and rise less.