The 2014 election in Texas illuminated the burdens of voter-ID laws. Because of the law—the strictest in the country—many longtime voters were turned away from the polls and unable to vote.

The Texas voter ID law is once again before a court on Tuesday, when the US Court of Appeals for the Fifth Circuit will consider whether to uphold a lower-court decision striking down the law as an “unconstitutional poll tax.”

The debate over voter ID in Texas is like a bad movie that never ends. A federal district court first blocked the law in 2012, a decision that stood until the Supreme Court gutted the Voting Rights Act a year later, freeing states like Texas from having to approve their voting changes with the federal government.

Following a lengthy trial, the law was struck down for a second time in October 2014 by Judge Nelva Gonzales Ramos of the Southern District of Texas, who found that 608,470 registered voters in Texas lacked the required voter ID, with blacks and Hispanics two to three times more likely than whites not to have one. She found that the Texas legislature passed the measure “because of and not merely in spite of the voter ID law’s detrimental effects on the African-American and Hispanic electorate.” Ramos’s ruling had significance far beyond Texas—her finding that the law was purposefully discriminatory meant that the state could once again have to clear its voting changes with the federal government.

That decision stood for only five days before the conservative Fifth Circuit reinstated the law for the 2014 election, faulting Ramos for blocking it so close to the election. The Supreme Court affirmed the appeals-court decision three weeks before the election—the first since 1982 that the Court had declined to block a voting measure deemed intentionally discriminatory by a trial court.

The Brennan Center for Justice has been compiling the stories of dozens of Texas voters who were prevented from casting ballots in 2014 because of the voter ID law. (See here and here and here).

They are heartbreaking to read and often border on the absurd.

Daniel Menchaca, 61, lives in El Paso and has worked at a federal agency office in Texas for the last 31 years. He participates in elections regularly, and has been voting at his precinct in a local fire station for many years. This time, when he went to the polls, he was not allowed to cast a regular ballot on Election Day because he did not have his Texas driver’s license with him.

He did have multiple forms of identification at the polls. In addition to his voter registration card, Mr. Menchaca had a government-issued photo identification card: his federal civilian-worker identification from his job at a federal agency. This ID has his picture and an expiration date, he needed to undergo thorough background checks to receive it, and he uses it to get on a military base—which includes a missile range—for his job. Despite both of these forms of identification, however, he was forced to vote provisionally. When he showed his ID, the poll worker told him that “a lot of federal workers are foreigners.”

Mr. Menchaca was instead forced to vote a provisional ballot. However, he was not able to provide the additional documentation needed to make it count in time—in part because the process for doing so was not explained to him. “They made it sound like I just had to fill it out and put it in the box and it would count,” he said. Ultimately, despite showing up at the polls with multiple forms of identification, his vote did not count.

“I always keep that ID clipped to my shirt, and the military police check it, and look at my face, and verify that I’m on the list, before I can get on the base. My ID is good enough to get on a military base, but it’s not good enough to vote?”

Such stories were far too typical in 2014.

Della Lewis is 89 and lives in Montgomery. She has been voting since she was 30 years old, and has never had any problems—until 2014. “They always sent me my card and I always voted,” she said. But she couldn’t vote last November because she did not have an up-to-date photo ID. She no longer drives, so her driver’s license is expired. Even with her voter registration card, she was not allowed to vote.

She voted a provisional ballot, but she was not able to get it counted. She could not get to a Department of Public Safety (DPS) office with the documentation she needed in time to have her vote counted. She does not have access to a birth certificate, because she was delivered by a midwife, and she was not able to get the other documentation she would have needed to get a new ID in time.

“They know I’m Della Mae,” she said. “If they weren’t going to count my vote, why do they keep sending me a voting card?”

Dorothy Rains-White is 87 and lives in Huntsville. She has lived in Texas all her life. She needs a cane or a walker to get around. When she went to vote with her husband, Willis White, she was unable to cast a regular ballot because they would not accept her expired driver’s license (she no longer drives).

Getting the provisional ballot counted proved impossible. The last time they tried to get her a driver’s license, according to Mr. White, there was a “big ol’ form” for her to fill out and a whole set of documents required. Mr. White said the DPS did not tell them anything about the possibility of getting a free ID card—and instead said they would have to pay a fee to get a new ID.

Mr. White also observed that trips to the DPS can be difficult. There is no place for older people to sit down while they wait. Mr. White saw a pregnant woman who waited three hours and still was not able to get an ID—she was in tears.

Mrs. Rains-White was upset by the experience. She said “I have been living in the state of Texas all of my life and I felt like I had been cheated out of the privilege of voting.”

Those who believe that voter-ID laws are not preventing people from voting need only look at Texas for a strong rebuttal. Over 600,000 registered voters lack a voter ID, but the state issued only 407 IDs as of Election Day 2014. (You can vote with a gun permit in Texas, but not a student ID.) The state official in charge of distributing voter IDs told his coworkers that “zero is a good number” of requests. Even with a high-profile governor’s race in 2014 between Greg Abbott and Wendy Davis and a record number of registered voters, Texas had the second-lowest voter turnout rate in the country in 2014, with 300,000 fewer ballots cast than in 2010.

The three-judge panel hearing the voter ID appeal on Tuesday includes an Obama and Clinton appointee, increasing the chances that the law will be struck down. But any decision can be appealed to the full Fifth Circuit, which is dominated by conservative Bush and Reagan appointees. Whatever the Fifth Circuit decides, the case is likely headed to the Supreme Court.

When it stuck down Section 4 of the Voting Rights Act in June 2013, the Court’s majority claimed the remaining provisions of the VRA would sufficiently protect voters from discriminatory voter suppression efforts. Texas will provide the ultimate test of whether that’s true.