Due to the space restriction on mounting points because of the need for the chair to move, recliner arms tend to be mounted only on one wooden rail, which leads to an inherent weakness in the design. A loose arm, although it can be caused by loose bolts, is normally due to the wooden mounting rail sheering from the arm frame. Access to this is via removal of the material (or leather) and removal of the recliner metal action. It's a huge job that is beyond most DIYers.
Richard Oldroyd
October 2014
Automatic Answer
While you wait for answers, we may have found some information which could help you.
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix chairs.