All triggers follow the same timing rules, whether they are defensive triggers or other action triggers. Summarized:
Immediately - They resolve when you declare the trigger.
When resolving - They resolve when you resolve the other effects of the action or ability.
After killing - When/if you kill the target of the action, as part of resolving the damage.
After resolving - After the action is completed, whether successful or not (but only if the model is still in play or, if the trigger has a target, if the target is still in play).
After succeeding - Same as "after resolving" but only if the duel was successful.
If no timing is listed, the default is "after succeeding."
So, for "when resolving" and "after resolving", the trigger's effects happen whether or not you win the duel.