To take a page from Dogs in the Vineyard, Step One of a conflict is to establish what's at stake. The stakes should be agreed upon by the GM and the players before initiative is rolled, so to speak, informed by the circumstances that surround the conflict and the personalities of the participants. Sometimes, one side has the other at a disadvantage and can get away with seeking higher stakes, but that's just another factor to consider when negotiating. For example, if a pair of insane vampires have captured a wounded PC, they have the advantage and can seek high stakes. However, if the PC knows that help will be on the way very soon and he merely needs to stall, then the PC's player can refuse to accept those high stakes and negotiate something more acceptable. Role-playing is a significant factor at this stage.
Once the Stakes are agreed upon, then the die-rolling portion of the conflict should take place. If one side Concedes or gets Taken Out, then the other side wins those Stakes. If, for any reason, one side decides mid-scene that they want to fight for a different set of Stakes, then another conflict would need to be initiated, possibly with a cleared social stress track.
It is also important to remember that mere force of personality (as represented by a character's social skills) sometimes just isn't enough to win certain stakes. Without genuine bargaining chips, some stakes will simply be out-of-reach, no matter how superb their Intimidation or Rapport skills are. As with the above example, if the player decided that nothing short of bloody violence would convince their PC to give up their quest to rescue a loved one (i.e., "I'll save her or die trying") and the GM doesn't have any additional bargaining chips to put on the table, then simple social conflict cannot be used to win that stake.