Sarah Hekmati's young son had it all figured out. He'd burst into Iran's notorious Evian jail with Superman and Batman and free his uncle to bring him home to the United States.

At this point the family of Amir Hekmati feels it may need superhuman intervention to free the former US Marine, who has been imprisoned in Iran since 2011.

"We've been struggling for four years now, and we're just exhausted," Sarah Hekmati told AFP on Sunday, describing how her brother's incarceration has taken its toll on the family with her father now terminally ill, and her young children unable to grasp why their uncle is being held by Iran.

Amir Hekmati, 31, who was born in the United States to parents of Iranian origin, was on his first trip to Iran to visit his grandmother when he was arrested in August 2011 shortly before he was due to leave.

Initially sentenced to death for espionage, Iran's top court subsequently reduced the charges and his penalty to 10 years in prison.

But the fates of Hekmati and three other Americans -- Saeed Abedini, a Christian pastor, Washington Post journalist Jason Rezaian, and retired FBI agent Robert Levinson who disappeared in Iran in 2007 -- have all unwittingly become tied to higher diplomatic stakes being played out in Vienna.

And they remain a potent symbol of the myriad of lingering concerns which the West still has with Iran -- from human rights abuses to its alleged sponsorship of terror groups in the Middle East -- even as global powers seek to tie down a nuclear deal.

Sarah Hekmati and her husband Ramy Kurdi arrived in Vienna this week and will stay through Tuesday's deadline for a nuclear deal, in the hopes of raising the profile of her brother's case. Ali Rezaian, the brother of Jason, was also in Vienna this week.

"We really need to gain momentum and gain leverage, while they (Iran and the US) are sitting across the table from each other," Sarah Hekmati told AFP.

The family have pleaded in letters with Iranian leaders to release Hekmati as a humanitarian gesture during the holy month of Ramadan.

Their father, Ali, is now dying from a brain tumor. "Time is not on our side. My father is suffering," said Sarah Hekmati.

- Health concerns -

But a request to meet with the Iranian delegation in Vienna headed by Foreign Minister Mohammad Javad Zarif has so far gone unheeded.

The Michigan family are also increasingly worried for Amir's health as he seems to have been suffering from a stubborn respiratory illness for almost the past year.

They say Iranian officials told the State Department two years ago that under Iranian law Hekmati was eligible for amnesty from his third year. And they insist his case should not depend on the outcome of the nuclear talks.

"Let's say the 30th comes and things fail or they go in the wrong direction, I don't want my brother to continue to languish for something that has nothing to do with him," Sarah Hekmati said.

American TV personality Montel Williams, also a former Marine, has also now taken up Hemakti's case, seeking to draw greater attention to his plight across the United States and "trying to make sure their voice is heard."