A friend and I spawned the wither, and while we were fighting it, I died and respawned and was on my way back to where the wither was to help my friend when he died and respawned back at our house, and when we both arrived on scene to try to continue killing the wither, no attacks would result in the wither taking damage.  My friend shot him with a bow multiple times, and he changed color to red (similar to what happens when mobs take damage), but his health bar would not reduce.  I got close enough to hit the wither with my enchanted diamond sword and got 8 good hits in, and each time, he flashes red like he takes damage, but the health bar does not reduce.

The wither destroyed most of that area of the map, and I after 30 minutes of dying, continuing to put on armor, run over to where the wither was located with our diamond swords, and trying to kill it,  I eventually had to turn on cheats and use a kill command to kill it because it wouldn't take damage.