  The Neptune Trojans are the most recent addition to the panoply of Solar
system small body populations. The orbit of the first discovered member, 2001
QR$_{322}$, was investigated shortly after its discovery, based on early
observations of the object, and it was found to be dynamically stable on
timescales comparable to the age of the Solar system.
  As further observations were obtained of the object over the following years,
the best-fit solution for its orbit changed. We therefore carried out a new
study of 2001 QR$_{322}$'s orbit in 2010, finding that it lay on the boundary
between dynamically stable and unstable regions in Neptune's Trojan cloud, and
concluding that further observations were needed to determine the true
stability of the object's orbit.
  Here we follow up on that earlier work, and present the preliminary results
of a dynamical study using an updated fit to 2001 QR$_{322}$'s orbit. Despite
the improved precision with which the orbit of 2001 QR$_{322}$ is known, we
find that the best-fit solution remains balanced on a knife-edge, lying between
the same regions of stability and instability noted in our earlier work. In the
future, we intend to carry out new observations that should hopefully refine
the orbit to an extent that its true nature can finally be disentangled.
