It's very common for people to have a strong side and a weak side when it comes to riding. I'm stronger on my left side and usually ride better going to the left. :) Sounds like your left side might be the weaker side, as losing stirrups is often a sign of an unsteady leg. There could be several things happening... first of all, are you stirrups even? Most people's left stirrup is a little longer because they get on on the left side and stretch it out faster. Is your left leg a little shorter then your right? (it happens) You could try shortening it a hole and seeing if that helps. Are you putting more weight into your right seatbone or stirrup? Or are you collapsing your spine to the left (which will put more weight into your right side) This sounds like a random question, but do you wear a purse and do you hang it off your right shoulder? A dressage trainer told me that a lot of women normally hang their purses off the same shoulder, and it makes them carry themselves differently, even in the saddle. So if you carried it off your right shoulder, it would cause you go with your right shoulder a little higher then your left. It sounded wierd to me at first, but it's amazing how often I see it's true!