(CNN) When Tomeu Vadell, an American oil executive, was summoned to Venezuela for an emergency work meeting the week before Thanksgiving 2017, his wife said she urged him not to go.

"He was really overworked and tired," his wife Dennysse Vadell recalled. "He just said -- this is how good a person he is -- he just said, 'Well, this is the first time I have to make a trip in this new position that I have, I can't just say that I can't go.'"

She said neither he nor their family suspected what would happen next.

Tomeu Vadell and five other Citgo executives -- Gustavo Cardenas, Jorge Toledo, Alirio Zambrano, Jose Luis Zambrano and Jose Angel Pereira -- were arrested and detained on corruption charges. Citgo is the US subsidiary of the Venezuelan oil and natural gas company PDVSA.

Tomeu Vadell is seen in an undated photo before his detention and in January 2019 in Caracas, Venezuela.

"We had no idea that something like this would happen and I'm still today thinking, how is this possible?" Dennysse Vadell said in an interview with CNN. "It's worse than a nightmare."

That was more than 600 days ago, and the six executives, nicknamed the "Citgo 6," remain in one of Venezuela's most notorious detention facilities. They have yet to stand trial and were only granted a preliminary hearing in June. Following their arrest, embattled President Nicolas Maduro said that they would be tried as "traitors."

"These are people born in Venezuela, they're Venezuelan and they're going to be judged for being corrupt, thieving traitors," Maduro said in a televised address in November 2017. Five of the six men are US citizens; one is a US legal permanent resident.

Efforts by the US government to free the men have been unsuccessful and complicated by the precarious political situation in Venezuela. While the Trump administration has stepped up its public advocacy on the case, the Vadell family said they are concerned that not enough is being done to secure Tomeu Vadell's release -- and they are worried about how much longer he can stand to be imprisoned.

'I didn't recognize him'

"It's worrisome for us because we're not getting any younger," Dennysse Vadell said. "The way they treat them is very bad. It's like the mental torture. It's not good for him."

Tomeu Vadell will turn 60 in mid-August and had some ongoing health problems prior to his detention, the family said. Cristina Vadell, one of his three children, said that her father is "working on making sure he's strong, mind, body and spirit."

"That's like his mantra. And knowing him, he's persevering in a way that I can't even understand or imagine, but the body still has physical limitations," she said in a recent interview with CNN.

He has lost so much weight, the family said, that Dennysse, who has been married to him for more than 30 years did not recognize him on the first of two visits she made to Caracas.

"I went inside this big room where there were about 10, 12 detainees and I went in and was looking around for my husband. I didn't recognize (him), it was until he went, 'Hey Dennysse, I'm here,' when I knew it was him," she recounted.

"I had to swallow hard not to show my shock to my husband because truly it was horrible," Dennyssee Vadell said, noting that he had lost "60 pounds" and that his hair had been shaved. "I felt him when I hugged him and it's heartbreaking."

Tomeu Vadell and his dog, Sargent Pepper, in Lake Charles, Louisiana.

The General Directorate of Military Counterintelligence (DGCIM) -- the agency where the Citgo 6 are being held -- has "been responsible for arbitrary detentions, ill-treatment and torture of political opponents and their relatives," according to a recent United Nations report. That report found that DGCIM "routinely resorted" to torture practices "including electric shocks, suffocation with plastic bags, waterboarding, beatings, sexual violence, water and food deprivation, stress positions and exposure to extreme temperatures" in order to "extract information and confessions, intimidate, and punish the detainees."

On Friday, Secretary of State Mike Pompeo announced the US was designating Ivan Rafael Hernandez Dala, the commander of DGCIM, and his immediate family members for his "involvement in gross violations of human rights." They will be ineligible to travel to the United States. The US sanctioned both the agency on July 11 and four DGCIM officials on July 19 for the torture and death of Venezuelan Navy Captain Rafael Acosta Arévalo.

"Our main concern is his health and his safety and it just seems like such a volatile place right now we just don't know what to expect," Cristina Vadell said.

'The names of all of them deserve to be known to the world'

The Trump administration has stepped up its public advocacy of the case. The State Department has issued two statements recently demanding their release. Special Presidential Envoy for Hostage Affairs Robert O'Brien on July 20 called for the immediate release of the Citgo 6 in a tweet related to the DGCIM sanctions.

"Those holding them are fully accountable for their safety. If the #CITGO6 are released, we would be grateful," he wrote.

Vice President Mike Pence met with family members of the detained men in April.

"On behalf of President Trump, our entire administration, and all the American people, I want to assure you that we're with you, and we're going to stand with you until your loved ones are free and until Venezuela is free," Pence said at that meeting. "The names of all of them deserve to be known to the world."

Tomeu Vadell and his family on Thanksgiving 2015 in Lake Charles, Louisiana. From left: Cristina (daughter), Tomeu, Dennysse (wife), Veronica (daughter), Diego (son), and Hayes (Veronica's husband).

However, administration efforts to free the men have thus far been fruitless. The US no longer has diplomatic relations with the Maduro government. American diplomats were ordered out of Venezuela in mid-March and a protecting power agreement with Switzerland is still not operational, so the men are without consular access.

The opposition faction led by Juan Guaido, whom the US has recognized as the leader of Venezuela, is aware of the Citgo 6 case. Guaido's ambassador to the US, Carlos Vecchio, said that they are seeking the release of all political prisoners. It was not clear whether they had raised the case in recent mediated negotiations with Maduro's government in Barbados.

Cristina Vadell said the family remains "looking for support from anyone that can help."

"I would hope sooner rather than later any and all the key stakeholders would come together, understand and release my father, an innocent man," she said.

'You want to think that they're doing everything possible'

The Vadell family told CNN that they feel "it's really hard to know" if the government is doing everything it can to secure the men's release.

"A lot of what we get is fairly general from the government. So to feel 100% comforted with that is difficult because you don't get to know everything about what may be happening. You want to think that they're doing everything possible, you want to believe that, but you don't know," Cristina Vadell said. She said they have also been working with members of Congress on the case.

The State Department did not reply to CNN's inquiry about the family's concerns.

Jason Poblete, a Washington, DC, area lawyer working with the family, noted that "these cases are very challenging because there's a lot of competing equities."

"You have so many different policy priorities. There's always going to be this tension almost kind of built into these cases," he said.

"It's helpful that the administration is starting to speak publicly about these cases and stressing to the stakeholders in Venezuela, be they Maduro or be they the opposition or anybody else who wants to help, this is a priority that these people come home," he added.

Poblete told CNN he believes Congress and the administration are "going in the right direction," but that "they just need to ratchet up the political will to bring these men home, bring Mr. Vadell home."

In a statement, a Citgo spokesperson told CNN that they are "are deeply concerned about our former executives who are detained in Venezuela."

"We support the efforts of the U.S. Government, including the State Department, to secure the release of these individuals. We pray for their safety and for their families who desperately wish to hear from their loved ones," the spokesperson said.

PDVSA and the Venezuelan government did not reply to CNN inquiries on the case.

'I just want him to stay strong'

Tomeu and Dennysse Vadell on their wedding day, February 1986, in Caracas, Venezuela.

The Vadells rely on the other families who have relatives in Venezuela who are able to visit for updates. Cristina Vadell said her father is supposed to meet with his lawyer weekly, but those visits are sometimes canceled. He has only received two visits during his detention, both from his wife, because the facility only allows family visitors and the Vadells don't have family members left in Venezuela.

Both Dennysse and Cristina Vadell described Tomeu as kind and hardworking.

"He's such a fun person to be with. He's got this great sense of humor," Dennysse Vadell told CNN. "I miss him so much. I feel totally incomplete without him."

The last time Cristina Vadell saw her father was November 2017, and she hasn't heard her father's voice since March, when phone calls from DGCIM were stopped. Asked what message she would send to her father, she said she "would tell him that I love him very much, that we all love him very much and that we're doing everything possible."

"I know he knows all these things and I just want him to stay strong, to remember, and know that we're just so proud of him for how strong he's been and to keep pushing, that this is going to end," she said.