
Any lunar satellite needs fuel to do regular orbit corrections, and when
its fuel runs out it will crash within months.  The orbits of the Apollo
motherships changed noticeably during lunar missions lasting only a few
days.  It is *possible* that there are stable orbits here and there --
the Moon's gravitational field is poorly mapped -- but we know of none.

Perturbations from Sun and Earth are relatively minor issues at low
altitudes.  The big problem is that the Moon's own gravitational field
is quite lumpy due to the irregular distribution of mass within the Moon.