  We consider the question: can the isotropy representation of an irreducible
pseudo-Riemannian symmetric space be realized as a conformal holonomy group?
Using recent results of Cap, Gover and Hammerl, we study the representations of
SO(2,1), PSU(2,1) and PSp(2,1) as isotropy groups of irreducible symmetric
spaces of signature (3,2), (4,4) and (6,8), respectively, describing the
geometry induced by a conformal holonomy reduction to the corresponding
subgroups. In the case of SO(2,1) we show that conformal manifolds with such a
holonomy reduction are always locally conformally flat and hence this group
cannot be a conformal holonomy group. This result completes the classification
of irreducible conformal holonomy groups in Lorentzian signature. In the case
of PSU(2,1), we show that conformal manifolds of signature (3,3) with this
holonomy reduction carry, on an open dense subset, a canonical nearly
para-Kaehler metric with positive Einstein constant. For PSp(2,1) we also show
that there is an open dense subset endowed with a canonical Einstein metric in
the conformal class. As a result, after restricting to an open dense subset the
conformal holonomy must be a proper subgroup of PSU(2,1) or of PSp(2,1),
respectively. Finally, using a recent result of Graham and Willse we prove the
following general non-existence result: for a real-analytic, odd-dimensional
conformal manifold, the conformal holonomy group can never be given by the
isotropy representation of an irreducible pseudo-Riemannian symmetric space
unless the isotropy is SO(p+1,q+1).
