Clinton's recovered emails will eventually end her run for the presidency. She is being investigated by both the CIA and FBI. If she cannot be trusted to follow the rules when it comes to a simple email account, people will not see her as trustworthy enough to run this country.
In my opinion, a few mishandled emails will not end her run towards presidency. This was an issue that was going on before the race got this far in, and it really hasn't been brought up as a reason why she couldn't handle a presidency. Her opponents seem to focus more on what they'd like to work on rather than slinging mud on her campaign over this. I feel that the opinion of the people will prevail more in regards to this as it's public knowledge those who research and understand the people running will be the ones to vote in the election in November, and they will be the ones that understand the implications of a technological lapse of judgment.
In trying to take Clinton down, the Republicans have become the boy who cried wolf. With Benghazi and these emails, any scandal affecting Clinton has become a case of the opposition trying to take her down. Ironically, the best way to do that would be with her policies and inconsistencies, but then these arguments have never been about actual politics.
Yes, Mrs. Clinton used her power as the first lady to do many things, including setting a secret email server when her husband, Bill Clinton, was the President of the United States of America. She may compose millions of emails with that server, and she deleted a lot of them. Her excuse of deleting personal emails may not be a good one, but the US citizens will expect what she can do to the country as the President, not look back her past too much to dig her mistakes.
Hillary Clinton has cut every single deal she can possibly cut, and has come too far to allow a breach of national security stop her. She'd kill a man, (or four, in Benghazi's case) if it would help her chances at getting that presidency, and she won't lose a single ounce of sleep. I'm not voting for her, but she'll find a way to weasel out of this, and all the while, people will say she's such a promising candidate.