I looked at a diagram for the Pietta 1851 which shows the arbor held in place by a "base pin" at the rear of the frame (under the hammer). I'm guessing the base pin is driven it to hold the arbor in place (?). I'm going to give it a couple taps with a punch to see if it tightens it up.
http://www.vtigunparts.com/store/sho...etta+1851+Navy