  If $\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate
(in the infinitely many sites model) then it is well known that for each $t>0$
the measure $\mathbf Y_t$ is purely atomic with infinitely many atoms. However,
Schmuland proved that there is a critical value for the mutation rate under
which almost surely there are exceptional times at which $\mathbf Y$ is a
finite sum of weighted Dirac masses. In the present work we discuss the
existence of such exceptional times for the generalized Fleming-Viot processes.
In the case of Beta-Fleming-Viot processes with index $\alpha\in\,]1,2[$ we
show that - irrespectively of the mutation rate and $\alpha$ - the number of
atoms is almost surely always infinite. The proof combines a Pitman-Yor type
representation with a disintegration formula, Lamperti's transformation for
self-similar processes and covering results for Poisson point processes.
