Relatives of an African-American shopkeeper burnt to death in 1964 – apparently by the Ku Klux Klan – are demanding to know why there has been no progress in solving the case after a grand jury hearing was brought to a close this week having failed to reach any conclusions.

The expiry of the grand jury looking into the civil rights era murder of Frank Morris in the small town of Ferriday, Louisiana, has prompted expressions of anger and frustration from those involved in the case. Almost a half-century after Morris, 51, was set alight in a petrol bomb attack on his shop, legal experts and the victim's family are incensed that no charges have been pressed – despite the fact that a suspect in the killing has been identified still living in the region.

The cold case of Frank Morris was one of more than 100 civil rights era murders that have been reopened by a specialist unit within the US department of justice working with the FBI. Morris's case was reopened in 2007.

A grand jury has been sitting since February, led by federal prosecutors operating under Louisiana state law. The jury's term limits ran out this week with nothing to show for it, and a new grand jury will now have to be convened and start the process again from scratch.

"Why has this taken so long?" said Rosa Williams, Morris's granddaughter. "We just want to see justice done, to have closure, and we won't give up until we get it."

Williams was 12 when her grandfather died. "He was a good church-going man," she said. "No-one ever spoke anything bad towards my grandfather. I just can't understand why would want to set him on fire and burn him up."

Frank Morris was working in his shop on the night of 10 December 1964 when he heard the glass in the front window being smashed. He saw two or three men pouring petrol into the shop, and later told FBI agents from his deathbed that the men had told him: "Get back in there, nigger" and forced him back inside.

The store turned into an inferno and Morris rushed out of the back exit engulfed in flames. He was described by an eyewitness as a "human torch" and died in hospital four days later.

An FBI investigation into the murder was held at the time, but nothing came of it. Then, a few years ago, two law professors from Syracuse law school in upstate New York, Janis McDonald and Paula Johnson, began studying the case. They set up a unit, the Cold Case Justice Initiative, and with the help of their students and using the Freedom of Information Act they uncovered 7,000 pages of 1960s documents that threw up crucial leads.

Working closely with Stanley Nelson, the editor of Ferriday's tiny local newspaper, the Concordia Sentinel, the professors uncovered FBI records that pointed the finger of blame for the murder at the Original Knights of the Ku Klux Klan, the dominant KKK group in Louisiana at the time.

The FBI pointed the finger of blame at the Original Knights of the Ku Klux Klan, documents show. Photograph: Jessica Rinaldi/Reuters

Nelson and the Syracuse initiative linked the arson attack back to the deputy sheriff of the local Concordia parish, Frank DeLaughter, who was furious with the shoemender because Morris had refused to give him a free pair of cowboy boots. DeLaughter was later prosecuted for police brutality in an unrelated case, and died in 1996.

Other documents suggest that the Klan had it in for Morris because he ran a successful business that served both white and black customers, including white women.

In January this year, Nelson reported in the Sentinel that a man called Arthur Leonard Spencer had been implicated in the shoe shop attack. A truck driver, aged 71, Spencer today lives about 45 miles away from Ferriday.

The paper interviewed Spencer's son and his former brother-in-law, who both alleged that they had heard Spencer confess to having taken part in the arson attack. His former wife also came forward to allege that she had heard another Klansman name Spencer as an accomplice.

The son, Boo Spencer, told the paper that his father had told him that Morris had been "doused with gasoline and started to run". One of the Klansmen, Boo Spencer said, had shouted: "Run, nigger, run."

Arthur Spencer denied to the paper that he had anything to do with the attack, though he did admit to having been an active KKK member at that time. He has never been charged with any crime.

The Syracuse professors see the failure to move forward in the case as an indictment of the federal government's determination to tackle the many unsolved race killings of the civil rights era. The department of justice has in recent years reopened 111 cases involving 124 victims, and yet of those only five have led to successful prosecutions. More than 70 have been closed again without any resolution.

In some cases, the department says, the cases were closed because all suspects and/or witnesses have died; in others, there was insufficient evidence. In his most recent report to Congress on the handling of civil rights era cold cases, the US attorney general Eric Holder admitted that "very few prosecutions have resulted from exhaustive efforts" but insisted that the department's efforts had "helped to bring closure to many family members of the victims".

McDonald disagrees that there has been any closure in cases that have failed to be resolved. "In the Frank Morris case, we gave investigators several witnesses and there's no reason for the lack of progress. For the life of me it's impossible to explain why they aren't moving forward," she said.

Nelson, who has now published more than 100 articles in the Sentinel about the case, said that time was running out for justice to be done. Between the Frank Morris case and the suspected Klan murder in July 1964 of a 25-year-old porter called Joseph Edwards in the nearby Louisiana town of Vidalia, Nelson says that six important witnesses have died in recent years, one as recently as two weeks ago.

"It's frustrating that the investigations are taking so long and sometimes it's hard to understand why. The Frank Morris case was reopened in 2007 and now it's 2011, and every day that passes brings the fear that another witness will die."

The department of justice said that it could not comment on the Frank Morris murder as the investigation is ongoing.

Brad Burget, the district attorney in Concordia parish where the murder happened, said he could not second guess the federal authorities who were leading the investigation. But he said he wanted to see the homicide solved.

"Justice delayed is justice denied, so I would like to see this case solved as quickly as possible. The timeframe of the murder makes no difference – it's just as important today to have closure as it would have been if Frank Morris had died yesterday."