(CNN) -- Relatives of seven Americans missing since a tourist boat capsized off the coast of Mexico over the weekend remain hopeful that their loves ones will be rescued, a family spokesman said.
"If we know there are still people out there who are going to make the effort to search for them, then we maintain the hope that they're going to be found," said Frederick Han. His father-in-law, 52-year-old Donald Lee, and his wife's uncle, Al Mein, are among the missing.
More than 40 people were on a fishing expedition when the boat capsized early Sunday. One American tourist was killed in Sunday's accident in the Sea of Cortez, near Isla San Luis, Mexico, authorities said.
Family members have been asking crews to keep combing the waters off the coast of Baja California past 2 a.m. Thursday, when the search window is set to expire -- 96 hours after the boat capsized. Favorable weather conditions have increased the likelihood of their survival, Han said.
"The thing that's sending the family into the panic is watching as that search window starts to dwindle," Han said.
Both U.S. and Mexican officials are part of the search, as the boat was carrying U.S. citizens and Mexican nationals. Han said his family members have asked for U.S. authorities to play a greater role, and have been getting the word out about the situation on online at findourfathers.blogspot.com.
Few advances were made in Wednesday's search, the Baja California state government said. A U.S. airplane arrived with special equipment to help find the sunken boat, the government said.
In addition to Lee and Mein, Mexican authorities identified the missing as Russell Bautista, Mark Dorland, Brian Wong, Gene J. Leong and Shawn Chaddock.
Along with rescue officials, fishermen who were in the area Sunday helped save several people.
Mike Kalicki, a fisherman who was part of the effort, held back tears as he recounted the rescues.
"It was nice to be able to help out," Kalicki told CNN affiliate KGTV. "They look at us like saviors. We just helped them out. Later that evening, we all went to the beach and had a group hug."
Harry Edwards, a spokesman for the U.S. State Department, said Tuesday that so far 19 American passengers have been rescued.
U.S. authorities identified the U.S. tourist who died as Leslie Yee.
There were conflicting numbers on how many people were on the boat when it sank. Mexican authorities counted 43 passengers and crew, while the Coast Guard put the number at 44.
The state Attorney's General Office has opened an investigation into the incident, but no arrests have been made, according to the Baja California government.
Han said his father-in-law, a retired automotive parts specialist from San Ramon, California, was on a much-anticipated annual fishing trip to the area with a group of friends.
"He has his own boat. He was out on the waters very regularly. We know that being a strong swimmer, if he had a chance to really make a swim for it, he would," he said.
CNN's Catherine E. Shoichet contributed to this report.