It is probably one of the most difficult things the Coast Guard has to do: suspending the search for mariners lost at sea while loved ones implore them to keep looking for at least a little longer. Their hope is rock-solid, their pleas as heartfelt as any you’ll hear in your life, let alone your career.

And yet at some point, professional search organizations have to make that difficult decision to suspend after weighing the odds of survival against a host of factors, everything from water temperature and sea conditions to the survival equipment carried and the experience of those missing.

This tough situation has played out publicly over the last several days in the case of four missing British sailors, whose 40-foot sailboat Cheeki Rafiki capsized in rough seas more than 600 miles east of Cape Cod, Mass., late last week. After suspending the search Sunday morning, the Coast Guard resumed the search Tuesday amid growing public and political pressure.

An online petition urging the Coast Guard to continue looking for the sailors had garnered more than 200,000 signatures as of Tuesday. British entrepreneur Richard Branson, who had to be rescued in 1985 when the powerboat he was racing across the Atlantic sank, tweeted “urge for longer search for missing Cheeki Rafiki yacht.”

British Prime Minister David Cameron also expressed his gratitude that the search was resumed. “My thanks to the U.S. Coast Guard, which has resumed its search for our missing yachtsmen,” Cameron tweeted.

The hope is that the four experienced sailors are in a life raft, which would immensely increase their chances of survival.

Cheeki Rafiki has been identified as a Beneteau First 40.7 that was returning to the United Kingdom after competing in Antigua Sailing Week.

In addition to U.S. and Canadian aircraft, an RAF C-130 Hercules has joined the mission. There are also reports that a flotilla of more than 40 private vessels, some returning from the Antigua regatta, will scour the waters for the missing sailors. And at least five commercial vessels are taking part.

The Coast Guard was first notified about 12:30 a.m. Friday that emergency signals had been received from two 406 MHz personal locator beacons registered to Cheeki Rafiki, prompting a multination search of more than 4,000 square miles. The boat’s agent in the U.K. also told the Coast Guard that the last message it received from the crew on Friday said the boat was taking on water.

About noon on Saturday, the 1,000-foot ship Maersk Kure located a capsized sailboat believed to be Cheeki Rafiki. The Coast Guard said rescue crews spotted small debris fields, indicative that its search patterns were accurate. No signs of life and no life raft had been found, said the Coast Guard in a statement.

The so-called “active” search was suspended at 5 p.m. Sunday. It was resumed at 7:38 Tuesday morning about 1,000 miles east of Cape Cod.