I had thought of that but discarded it as kind of counter-logical. No thoughts on mending and similar spells?
Are you suggesting mending should heal them? If their statue-body is considered to be living once they animate it I suspect it stops being an object so the spell wouldn't affect it as per the RAW. However I have no objection to going along with "healed by mending" if you both fancy it.
That said, I could see them being affected by Construct-healing magic like repair spells, but I believe those non-OGL.