TEQUESTA, Fla.— Families hoped for a miracle even as science nagged that one was improbable and rescue crews went into a seventh day of searches Thursday for two teens missing at sea.

Though it seemed unlikely a medley of agencies would continue their hunts much longer, the Coast Guard, which is leading the effort, insisted it remained an “active and open” case now focused off the Georgia and South Carolina coastline.

Girls wear T-shirts they bought to help fund a private search for two Florida teens who remain missing after their boat was found capsized at sea.

Chief Petty Officer Ryan Doss said crews would continue surveying waters from Florida up through South Carolina throughout the day Thursday and overnight into Friday. A determination on plans for beyond that had not been made, but Doss said there were no immediate plans to call the search off since it was believed there was a chance the 14-year-olds, Perry Cohen and Austin Stephanos, were still alive.

Doss called the decision on how long to continue looking for the teens a mix of “art and science,” that juggles knowledge of how long people can survive adrift with unknowns on whether the boys had flotation devices and drinking water – and even the extent of their physical stamina.

Those following the story around the world lit up Twitter and Facebook with thousands of messages of support. People turned out at local vigils and more than $185,000 was raised online to fund a private search. Residents turned up as dusk fell on beaches and lit candles.

The saga of the two boys from Tequesta, Florida, began last Friday. Their parents believed their fishing outing would take them to a local river and waterway, as was the rule in previous solo trips, not to deep Atlantic waters. Summer storms moved through the area that afternoon, and when the teens didn’t return on time, the Coast Guard was alerted and began their day-and-night search.

The Coast Guard has covered a mammoth search area of nearly 40,000 square nautical miles, stretching from the waters off South Florida up through South Carolina. It has proven a frustrating ordeal, with no new clues since the teens’ capsized boat was located Sunday.

Stories of miracle rescues have popped up throughout history, though, and many were still hoping for one for Perry and Austin.

In 2005, two South Carolina teens were swept out to sea on their small sailboat during a storm. After searching for them for several days, the Coast Guard and state officials began referring to their effort as a recovery operation not a rescue. Yet the teens were found alive after nearly a week at sea. A key difference from the Florida teens, though: They were still aboard their boat.

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