Nue's randomly heal their health. It's happened to my group like 3-4 times from one Nue.
The way I kill those blasted Faeries is that I have them slightly higher than me (jump up and land to get that height). Then I duck (it'll miss [except the ring of fire]) and everyone else is behind it whacking it. If the faerie changes target then I get up and skill it until it attacks me again.