Comment 4 for bug 167168

If an object with the connector-avoid property is moved to
overlap a broken connector, the connector is "repaired" -
i.e., it connected to its endpoints again and routed around
all objects between. So, as a woraround, the user can create
a small object and just drop that on every broken connection.

Which inspires the following idea:
Maybe a quick fix would be to add a "re-route all
connections" button. I realize this has negative
consequences: If you have carefully reshaped your
connections with bezier curves, this will replace them all
with straight lines. But at least all connections will have
the right start- and end-points again. So it might be a
viable band-aid, until the correct solution has been figured
out.