(CNN) -- "This is the Charm Blow, we are abandoning ship."
With that message -- delivered at 4:20 p.m. Sunday -- radio communication between the boat and the Coast Guard went dead.
Since then, searchers have been scouring the waters off San Francisco for the reported occupants of a 29-foot sailboat -- a couple, their 4-year-old child and the child's cousin, who the Coast Guard said is younger than 8.
Coast Guard spokeswoman Pamela Boehland said the search will continue through the night.
The man had called the Coast Guard an hour earlier to say that the boat had begun taking on water and its electronics were failing, the Coast Guard said. At that time, the boat was some 65 miles (105 kilometers) off Pillar Point, south of San Francisco.
The four might have boarded a life raft, said the Coast Guard, which appealed to the public for help Monday in identifying the missing seafarers.
"We don't have a lot of information to go on," Boehland told CNN. "All we know is that there were those four people on board and the two young children, and we're hoping that there is still time to save them."
The focus of the search was 60 to 65 miles off Monterey Bay, said Lt. Heather Lampert, a Coast Guard spokeswoman.
Several aircraft and vessels have joined the search.
Asked about the possibility that the report could be a hoax, given that no one has come forward to identify a family as missing, the Coast Guard said that it operates under the assumption that such reports are legitimate.
If the boat did not have a life raft, the chances of survival are slim, said Mario Vittone, a recently retired Coast Guard helicopter rescue swimmer and a marine safety specialist. "They're not going to live long, even in life jackets," he said. "That's cold water out there."
According to the National Oceanographic Data Center, the water temperature off San Francisco was 49.3 degrees Fahrenheit (9.6 C).
Marine accidents in waters below 50 degrees F are five times more likely to end in death, Vittone said.
Computer models will factor in currents, weather and wind to create search patterns to focus searchers' efforts, he said.
The search will continue until the four are found or until the limits of survivability have passed, he said.