While fighting the wither, I got the wither down to half health. Once it gained its arrow invincibility, its health bar went from half health to no health. I continued to attack it with a sword up to what I can assume was more than half health but the health bar didn't change. I moved a few blocks until the health bar disappeared, then re-entered the zone where it was; however, the health bar no longer appeared and the wither seemed to have disappeared (I was still able to hear the wither). It was still shooting skulls at me, not from its original point, but a few blocks away from where i was regardless of where i went, as if the wither had become invisible.
I was playing on a survival world on Hard difficulty. The world was created before 1.9. The wither was also near the top layers of bedrock in the nether. Cheats, texture packs, and resource packs have never been enabled,
(Edit: After dying to the wither and waiting a few minutes, the wither is back with full health, but completely immune to arrows)
(Edit 2: the wither can still be killed afterwards. although the health bar was full, the health dropped back to half health as soon as I hit it with a weapon. perhaps the invisibility/invincibility was a bug, but the healthbar issue is definitely an error)