  Let $X$ be a complex manifold containing a hypersurface $D$ and let $D^s$
denote the singular locus. We study the problem of extending a flat connection
with logarithmic poles along $D$ from the complement $X \setminus D^s$ to all
of $X$. In the setting where $D$ is a weighted homogeneous plane curve, we give
a new proof of Mebkhout's theorem that extensions always exist. Our proof makes
use of a Jordan decomposition for logarithmic connections as well as a version
of Grothendieck's decomposition theorem for vector bundles over the `football'
orbifold which is due to Martens and Thaddeus. In higher dimensions, we point
out a close relationship between the extension problem and castling equivalence
of prehomogeneous vector spaces. In particular, we show that the twisted
fundamental groupoids of castling equivalent linear free divisors are
`birationally' Morita equivalent and we use this to generate examples of
non-extendable flat connections.
