It’s a simple question with no simple answer: Why do polling places across America keep running out of ballots when it’s no secret that this contentious primary season keeps breaking voter turnout records?

For one, even the best-made plans have gone awry; officials in state after state have ordered more ballots, only to see turnouts exceed their most ambitious estimates. Some states — California, for example — extended registration deadlines, in part to give would-be voters more time to sign up for the first Democratic presidential nomination race between a black man and a woman.

But some election officials say those extensions have necessitated a form of fortune telling when it comes to deciding how many ballots to order.

Not helping is the fact that ballot printing is a highly specialized field with a limited number of companies willing to take on the heavily monitored and time-consuming burden of producing and delivering voting cards. Price per ballot can range from 20 cents to more than $1, depending on complexity.

So with Pennsylvania’s important April 22 primary looming, and nine other state nominating contests scheduled for May, election activists wonder if even more voters could be subject to huge lines and disenfranchisement caused by an insufficient supply of ballots.

“We’re going to keep having this problem,” the director of the Election Center, which represents voting officials across the country, Doug Lewis, said. “Running an election sounds pretty simple until you try to do it. Folks just don’t understand how much advance planning goes into setting this up. “If you run out of ballots, it’s because your crystal ball isn’t good enough,” Mr. Lewis said.