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A once-hopeful search for a South Carolina man who went missing last week during a cruise excursion in Cozumel, Mexico, is dimming.

Edmond Bradley Solomon III's family, including his daughter and wife, have been using social media and physically scouring the island with several local law enforcement agencies, but promising leads have become dead ends and theories are running dry.

Solomon was last seen on April 3, when a Royal Caribbean cruise ship stopped in Cozumel, where he got off the ship, went to the bathroom and vanished, his family said.

"I am terrified that if I don’t post something our story will become irrelevant, and that the U.S. will forget about us," Solomon's daughter, Savannah Miller, wrote on Facebook. "I am trying to think of something to say to keep everyone updated, but I am feeling empty and discouraged and exhausted. 

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Edmond Bradley Solomon III, a retired VA critical care nurse, and his wife Mimi

Edmond Bradley Solomon III, a retired VA critical care nurse, and his wife Mimi. (Facebook)

"I thought I was already losing my dad to FTD (frontotemporal dementia), but being unable to physically locate him is 100x more traumatic than any degenerative disease."

Miller is referring to her dad's recent diagnosis of frontotemporal dementia, a group of diseases caused by progressive nerve cell loss that affects a person’s behavior and not memory.

Known as "Brad," the 66-year-old Charleston family patriarch was enjoying retired life after 20 years as a VA critical case nurse with his wife Mimi, who is also a nurse and a breast cancer survivor. 

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They were on a cruise, stopped for an excursion to spend the day on Cozumel, a remote island off the coast of Mexico, when his family believes he wandered off after using the bathroom within minutes of getting off the ship. 

His daughter and other family members quickly dropped everything and flew to the popular tourist spot to join Mimi and the search with local law enforcement. 

Rescue efforts for Edmond Bradley Solomon III in Cozumel, Mexico.

Rescue efforts for Edmond Bradley Solomon III in Cozumel, Mexico. (Conexión Urbana/Facebook)

Mimi, Savannah and Edmond (left to right) pictured together.

From left to right, Mimi, Savannah and Edmond Solomon are pictured together. (Savannah Miller)

After a week, Solomon is still missing, and the ups and downs from potentially hopeful tips that lead to nothing is wearing on the family's mental state. 

"It angers me that everyone else’s lives are continuing, but we are stuck in this horrifying level of hell," Miller said. "If you are in America, please continue to kick and scream about us to catch media and U.S. government attention so that we can be allocated additional search and rescue resources. 

"Empathy, selflessness, and the endless capacity to love are my dad’s most distinctive traits, and they are the ones that still linger despite his personality-stealing disease. If you know him, you know he would do this for you."

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Solomon's family and friends have been sharing missing posters with loving anecdotes about how "Brad" has helped them. Missing Persons of America, a Facebook group created by a military family, created its own missing person flyers in the U.S. to complement the official missing persons bulletin in Cozumel. 

Rescuers search throughout the island of Cozumel, Mexico, for Edmond Bradley Solomon III.

Rescuers search throughout the island of Cozumel, Mexico, for Edmond Bradley Solomon. (Conexión Urbana)

Official missing poster for Edmond Bradley Solomon III created by Cozumel police.

The official missing poster for Edmond Bradley Solomon III that was created by Cozumel police. (Cozumel police)

Missing person for Edmond Bradley Solomon III

A missing person for Edmond Bradley Solomon III flyer created by Missing People in America. (Missing People in America/Facebook)

Miller continues to plead with people in the U.S. and Cozumel to "spread the word."

"We are begging you to share this on socials, so that we can increase awareness and gain more news coverage. The more people who are aware, the quicker we will find him," she said.

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Local news outlet Conexión Urbana has been covering the search in Cozumel and shared photos with Fox News Digital. 

"Since the manifestation of relatives themselves, authorities have set up a search operation that keeps up to date, which has sparked the interest of citizens and the American community on the island, who have joined the search efforts," Conexión Urbana reported in a translated Facebook post. 

"The municipal Civil Protection authorities have expressed their total recognition to the solidarity of the community, however, urges the need that any civic action in this regard, should include the coordination and supervision of the authorities expert in the subject, in order to avoid endangering the safety of those in solidarity supporting these search efforts, especially groups seeking internship in the jungle or at risk areas on the island."

Edmond Bradley Solomon III (left) was with his wife, Mimi (center), when he went missing, his daughter< Savannah Miller (right) said.

From left to right, Edmond Bradley Solomon was with his wife Mimi when he went missing, his daughter, Savannah Miller, said. (Savannah Miller)

Search efforts for Edmond Bradley Solomon III have been going day and night since he went missing on April 3.

Search efforts for Edmond Bradley Solomon III have been going day and night since he went missing on April 3. (Conexión Urbana)

Edmond Bradley Solomon III is pictured with his wife Mimi

Edmond Bradley Solomon III is pictured with his wife Mimi. (Savannah Miller)

Miller told Fox News Digital they have been following local authorities' lead since they arrived on the island while coordinating their own public awareness campaign across social media platforms. 

However, the toll it is taking is becoming overbearing. 

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"I have asked those surrounding me in Cozumel not to keep me informed of specific search efforts, lead, or other information because it’s making me too anxious and upset. I don’t have the bandwidth or the energy anymore," Miller wrote on Facebook. 

Conexión Urbana reported a large-scale search earlier this week that included flyovers and ground searches with a rescue dog named Lune "in the most difficult (areas) to access," which included jungles and the surrounding areas.

Search and rescue efforts in Cozumel include dogs trying to trace "Brad's" trail.

Search and rescue efforts in Cozumel include doSearch and rescue efforts in Cozumel include dogs trying to trace "Brad's" trail. (Conexión Urbana)

Authorities in Cozumel, Mexico, are searching the most difficult areas to access, including jungles, according to local news outlet Conexión Urbana.

Authorities in Cozumel, Mexico, are searching the most difficult areas to access, including jungles, according to local news outlet Conexión Urbana. (Conexión Urbana)

What to watch for, from Solomon III's daughter

"My dad walks really fast, and he does not have eyeglasses on like he usually does," Miller said in a previous interview. "He will often nod his head down and focus on the ground while walking. The more anxious he is feeling, the quicker he goes."

He "generally has a calm or apathetic attitude, and will probably refuse help if offered, especially from a stranger," she said, which worries her and family that this trait, coupled with his fast-paced walk, makes him seem confident he knows where he is going.

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"But he is not," Miller said. "He is lost and scared. He cannot show or process emotions like a healthy person would. Unfamiliar people or situations are intimidating to him. He does not know how to respond and will avoid." 

She said everyone in Cozumel has been helpful and kind to her and her family.

Edmond Bradley Solomon III, the patriarch of the family, surrounded by loved ones during Savannah's graduation

Edmond Bradley Solomon III, the patriarch of the family, was surrounded by loved ones during Savannah Miller's graduation. (Savannah Miller)

In the U.S., family and friends set up a GoFundMe for the family.

"Between cancer and dementia, (Mimi and Solomon III) have been through so much in the last few years and yet Mimi still shows up every day to take care of others," the GoFundMe says. "Please help take care of Mimi and Brad."

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Miller said anyone in Cozumel should send tips to the Cozumel police. 

For anyone in the U.S., "we ask that they continue to share the story and sentiments about my dad if they know him to raise awareness and to stay positive."