If there is a power failure during and election conducted on electronic voting machines, voting would still be possible. Voters can always hand in a temporary paper ballot and vote the old fashioned way. With that being said, paper ballots could easily be manipulated. In truth though, I'm not certain voting machines aren't tampered with also.
Batteries are getting cheaper and electronics use less power every year. Laptops and smartphones work perfectly fine when they are not plugged in to the wall because they have batteries. Just get a battery or a gas generator and use that to power your voting machines when the power goes out.
It would be too hard to distinguish who voted for who if the power were to accidentally reset all the information and voting data. There would be no way to assure people that their votes went through successfully if there was a power outage and it might even cause an uproar.