  We consider irreducible logarithmic connections $(E,\,\delta)$ over compact
Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$
inherits a natural parabolic structure over the singular locus of the
connection $\delta$; the parabolic structure is given by the residues of
$\delta$. We prove that for the universal isomonodromic deformation of the
triple $(X,\,E,\,\delta)$, the parabolic vector bundle corresponding to a
generic parameter in the Teichm\"uller space is parabolically stable. In the
case of parabolic vector bundles of rank two, the general parabolic vector
bundle is even parabolically very stable.
