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In front of the pretty whitewashed chapel where prayers have been said all week, they gathered to lay a shrine to Madeleine McCann on Friday.
But yesterday as Madeleine should have awakened to her fourth birthday in a quiet Leicestershire village, the search for her seemed increasingly hopeless.
Portuguese papers reported that a man who fled with a woman after photographing young girls, a few days before Madeleine vanished, drove a car with British plates. They might be the same couple caught on CCTV at a petrol station at Lagos, near Praia da Luz, hours after the abduction. Another couple, possibly British, from the McCanns' holiday complex - the Mark Warner Ocean Village - were taken to a nearby police station - possibly for an identity parade in front of Madeleine's parents.
But would abductors really stop at the first petrol station just out of the resort? Or stay at Ocean Village, under the noses of police?
So Portugal's Policia Judiciaria (PJ) is abandoning its ground searches for Madeleine. They have reinterviewed Madeleine's parents in a major review of the evidence.
There is no telling how many clues have been under detectives' eyes all along but Stella Cash is certainly the kind of person who might have offered some of them.
She was working at the Duke of Holland bar, 100m from the place where Kate McCann, Madeleine's mother, made her fateful walk to look in on her daughter at 10pm.
Several Mark Warner guests dined at Cash's restaurant that night and she later drove home past the McCanns' corner apartment at 10.50pm but no police officer has questioned her about what she saw.
"I don't think I saw anything suspicious but then I don't [know] what they might call 'suspicious'," she said. Security was what Kate and Gerry McCann, a GP and cardiac consultant, had in mind when they and three other couples with children, settled for the complex. It was their first holiday of this kind.
They booked with a company which has a reputation for creating hermetically sealed, child-friendly English enclaves in the sun. The Ocean Club, set in the one-time sardine fishing village of Praia da Luz, is unlike other Mark Warner sites. It is set within the village and the McCann's ground floor apartment backs onto a crossroads. The McCanns' week was not the warmest but it had passed off well. There were tennis sessions on the two courts, where Madeleine stopped for a picture holding tennis balls, and a visit to nearby Sagres.
Kate and Gerry seem to have dined at the tapas bar with their group most nights - and this routine was probably a critical factor in their daughter's disappearance between 9.30pm and 10pm on their penultimte evening in Praia.
Amid all the rumour and counter-rumour surrounding the case, it is hard to resist the assumption that the McCann's evening routine was being observed and her abduction planned. The abductor gemmied up the louvre blinds on a rear bedroom window to make an entry. To have made that entry to a random apartment would have been very risky.
Once inside, a quick escape - not through the unlocked front door, in full view of Madeleine's parents, but through the window to a car in the adjacent street - was easy. The A22 motorway - which cuts across the Algarve - is 10 minutes away, at speed; the Spanish border 90 minutes.
The border might have been sealed off in time had the police been alarmed by the distress call from the Ocean Club. Instead, it took a desperate call to GMTV from a McCann family friend, Jill Renwick, to alert the Britain to the inaction. The British media piled into Praia and confrontation with a Portuguese police inspector insistent that Portugal's segredo de justica law prevented him from revealing anything to the press or even to the McCanns.
The McCanns are now relocated with three Leicestershire Police family liaison officers to an apartment near the one where Madeleine was snatched. It is unclear whether they have been digesting the scraps of information reported by the Portuguese papers, watching Sousa's chaotic appearances; or following TV stories about roadblocks from northern Portugal to the Spanish border - all of which yielded nothing. But their deepening sense of horror has been palpable in their occasional daily appearances - to place their twins, Sean and Amelie, in a creche, attend the local church or to make the same declarations of hope.
On Thursday, Kate McCann was visibly distressed and needed support into church by a friend for a service of hope for her daughter.
Praia da Luz, a village where 50 per cent of the population is made up of British expatriots, shares their horror. Many holidaymakers continued an apparently random and futile search for Madeleine, despite the police decision to call it off. "We're parents. What more can we do?" said one woman. "How can you possibly holiday?" said Maggie Allen, 56.
The posters which locals have issued around the bars and restaurants also reflect the random nature of the search efforts when the public, and not police, take control.
"Maddie McCann, white PJs, taken last night," reads one. Madeleine never answered to Maddie and her pyjama top was pink.
Crime experts like David Hill, a former National Crime Squad professional who helped write police procedures on kidnap scenarios, are convinced Madeleine has been abducted by a paedophile ring, or else in an organised attack by someone looking for a child, or to sell one for adoption. "'Paedophile ring' might sound dreadful but it doesn't necessarily mean that something awful will have happened to her," he said. "By continued detective work she can be reached."
Forensic officers will have used tape to pick up fibres and will be seeking DNA deposits from the abductor's perspiration or saliva. There might be fingerprints. It is likely that in a case of such high profile that forensic analysis will be complete by now and results checked against Interpol and Europol databases.
"Officers should also be tracing and eliminating every Ocean Village resident from the last few weeks and eliminating them," said Mr Hill.
CCTV cameras are few and far between here - one at the local supermarket, where one of many possible suspects was seen, is not functioning.
But a theory that a British couple captured by them may be under suspicion continued to gather momentum.
A man who said his daughter and other girls had been photographed by a man in the company of a woman in a Renault Clio with British plates at Sagres, near Praia, insists that the same woman was caught on CCTV cameras at a service station near Lagos (on the main A22 route to the Spanish border) on the night of Madeleine's disappearance. The couple had been staying at an apartment in Borgau, near Praia. After nine days it doesn't seem much to hold on to but Gerry McCann, shaking slightly as he read his statement, only has hope to hold on to.
"We will leave no stone unturned in the search for our daughter," he said.
- INDEPENDENT
