As with all politicians, credibility is vital. In order to maintain credibility politicians should not take actions that are easily spun as self serving. Before initiating the recount Stein started a fund raising effort to raise money to pay for the recount. Having raised the necessary funds, she continues to raise funds and opens herself to the argument that she is simply pursuing the recount to enrich the Green Party.
While Jill Stein may believe a recount will help her, recounts rarely change results. There have been very few instances in history of recounts of electoral votes actually resulting yielding a different conclusion than was reached after the first count. While recounts do have their merit, they are often costly and inefficient in terms of time.
Jill Stein knew that she wouldn't win the presidency even before she ran. She certainly doesn't think that a recount would help her win; she just doesn't want Donald Trump to be president and is going to do whatever is in her power to avoid that. Recounts in Wisconsin, Michigan, Pennsylvania and other key states could help achieve that goal.
Stein must have ulterior motives for wanting a recount, because she is in fourth place. It's not like she finished second and it was close. Rather, she likely is just upset and wants to help Clinton win. There is no way that millions of Americans voted for Stein and it didn't show in the original vote totals.