If a character is losing/loses the battle by removal (capture, discard, withdraw, etc.), you still have a chance to activate other abilities (such as Dominants, that curse that adds an evil character to battle, etc.) before proceeding to battle resolution.
If a character is losing by the numbers (my strength beats your toughness, etc.), you must play all Dominats or other abilities before accepting your character's defeat because as soon as you admit defeat and place your character into the discard pile the battle immediately proceeds to resolution (during which dominants cannot be played).
Hopefully that makes sense. ^_^