Does damage from Challenge (and similar non-combat abilities) persist until combat happens or the turn ends?

Ruling: Yes, damage from Challenge persists on units until combat resolves on any battlefield or the turn ends. The damaged unit does not need to participate in that combat to be healed.

Sequence:

• Challenge deals damage equal to each unit's might to the other
• Damage remains on both units
• When any combat occurs on any battlefield, damage is removed from all units at the end of combat
• Alternatively, damage is removed at end of turn

Nuances:

• Combat only occurs when battlefields are contested, not from abilities like Challenge
• A unit can be healed by sending a different unit to contest a battlefield and trigger combat
• If either unit involved in Challenge leaves the field before it resolves, no damage is applied because the might value is no longer available