Does commander damage reset if the commander changes zones and returns to the battlefield?

Commander damage is a cumulative life-total tracker tied to the specific commander and the specific player who received the damage. Once a commander deals combat damage to a player, that total is recorded and persists for the entire game, regardless of what happens to the commander afterward.

This is governed by the Commander additional rules (rule 903.10a): a player who has been dealt 21 or more combat damage by the same commander over the course of the game loses the game. The phrase "over the course of the game" is critical — it means the running total never resets, even if the commander dies, is exiled, returns to the command zone, bounces to hand, or re-enters the battlefield repeatedly.

The commander's identity persists through zone changes because of the 'commander' designation, which is a property that follows the object regardless of zone (CR 903.3). When it returns to the battlefield, it is technically a new object (CR 400.7), but the damage log in the Commander rules is tracked outside of normal object identity — it's a game-wide historical record, not a property of the card object itself.

Concrete example: Your Ur-Dragon commander deals 12 combat damage to an opponent, then gets destroyed and you re-cast it from the command zone. Next turn it connects for 9 more damage to the same opponent. That opponent has now received 21 total commander damage from Ur-Dragon and loses the game immediately — the 12 from before was never erased.

There is no mechanism in the rules to reset commander damage short of a card that explicitly resets game history or removes the damage record, which no currently legal card does.