"As there is nothing to suggest that Madeleine is not alive," says Kate, "we have to keep looking for her. We all know there are cases of missing children, presumed dead, who have been found alive years, sometimes decades, later."
Little by little, they have schooled themselves not to dwell on the lurid possibilities that tormented them in the early days - that their daughter had been snatched by a paedophile network or met with a cruel death - but they are never free of questions, and sometimes they are ambushed by old fears.
"None of the scenarios is good when your child has been taken," she says. "You're in a dark place some of the time. You get upset. You get angry. I have spent hours thinking of the possibilities. Do I want to know what happened? I've sat myself down and asked myself: if you knew and it was truly awful, would that help?"
Her familiar sharp-boned face looks weary. At 45 she is pretty, but lines of anxiety show at her mouth and crease her forehead. She seems like a person suspended. Although she says she and Gerry are "in a better place" than at any time since Madeleine was taken, her sentences sound as though they are coming from a long way off.
"Living in limbo with this void and uncertainty is truly dreadful. It's hard to rest, to find peace. It's unsettling and uncomfortable all the time. Even on a 'good' day, that feeling is lurking. And of course you can never stop until you know; you're on a treadmill you can't get off. It's draining. Until you know, there is no true peace. We need to know for us and we need to know for Sean and Amelie so that, God forbid, in another 10 years or so they don't have to cope with this distressing limbo, too."
For the moment, Madeleine is as real to them, and to the whole family, as an absent person could be. They talk about her all the time, observe her birthdays with a party and gifts, give her Christmas presents and fill a keepsake box with things they think she would like - drawings, school work, sweets, a leaf.
There are photographs of Madeleine everywhere. Her room at the family home in Leicestershire is as she left it when they went on holiday, plus the unopened presents.
Kate opens and closes the curtains twice a day and sometimes stays to absorb what she can of Madeleine. It is not what everyone would choose to do, she agrees, but it is her way. Sean and Amelie still share a bedroom. Soon there will be the practical issue of what to do with a "spare" room one of them may need. "But that was the room she left and it would be familiar to her. It would be hard to dismantle it."
Cardiologist Gerry, 44, has a more practical turn of mind. "So in time we may perhaps look at it differently."
The twins' understanding of what happened in Praia da Luz on the night of May 3, 2007 is matter-of-fact and unafraid. "We explain it like a burglary," says Kate. "You must never take something that doesn't belong to you. Madeleine belonged to our family and someone who had no right to her took her away. We also explain that this is very rare. It doesn't happen every day."
Throughout that disbelieving summer, the international news was dominated by a single crime and a single small face. Madeleine was snatched from her bed between regular checks made by her parents, who were dining with friends in a tapas bar 50m away from the apartment. They thought the arrangement was so normal, so ideal, that they never questioned it, and plenty of sympathetic parents told them they would have done exactly the same. There were accusations of neglect, too, but no one was harder on the couple than themselves.
"We thought we had worked out the best plan," Kate says. "It seems very different now. I have persecuted myself about that decision for years, even though deep down I knew I was a caring parent and how much I loved my children."
In the early months, even years, she despised her daughter's unknown thief. "The thought of her feeling fear and wanting and needing her mummy and daddy provoked so much pain. It still does, when I wander down that particular path."
Kate is a practising Catholic, and when asked about forgiveness she used to say she needed to understand the motive. Now, tentatively, she feels differently.
"I think I could probably forgive Madeleine's abductor whatever the circumstances. I don't know whether it's simply because I'm stronger or because there's no benefit in not forgiving someone. I can't change anything and I don't want to be eaten up by hatred and bitterness. And maybe there is an element of pity - what kind of person could do something like this? Of course, forgiveness will always be easier if there is remorse."
The Scotland Yard review of the case, set up two years ago, relieves the McCanns of the burden of maintaining the search through private investigators.
"Emotionally, it helps," Kate says. "We were doing so much ourselves. Now at least it is not totally down to us. We have been able to switch off a little bit. If we go away, we know there is work going on. We are encouraged by what the Met team has done and found. They have uncovered so much."
Thirty officers are working full-time on Operation Grange. "As time goes on, it is hard to maintain the level of motivation but, if anything, they are more determined now. But we still want the Portuguese police to reopen the investigation [closed in July 2008]. We want to find our daughter and the person who committed this very serious crime."
Meantime, there is no let-up in the McCanns' fundraising and awareness campaign Find Madeleine (whose 10th birthday is on May 12). Their all-consuming focus is, and has been, astonishing. Kate, a former GP, has become an ambassador for the charity Missing People, which supports the families of some of the 250,000 who go missing in Britain each year. A transition, maybe, from personal grief to a concern for people whose bleak stories do not make the headlines. "Before Madeleine went missing," she admits, "I was horrifyingly ignorant about this issue myself. It really is much bigger than people realise."
Kate aims to raise £20,000 ($36,000) for the charity by running the London Marathon on Sunday.
Jo Youle, chief executive of Missing People, says "Kate's perseverance is truly inspirational. For families like hers, facing the toughest time of their lives when a child goes missing, Kate's marathon gives hope."
There are other reasons to be thankful. Once, Kate McCann was afraid that the intensity of grief would threaten their marriage, because she could not bear to take pleasure or comfort in the physical side of their relationship.
"I'm pleased, and relieved, to say our relationship is really good," she says. "Given that we've made it through so many awful things over the past six years - and not just made it through but are united, strong and very happy together - then we can make it through anything. We'll survive."
Nor are the many reported sightings of Madeleine as upsetting as they used to be. "I am able to rein in my emotions quite easily. [The reports] need to have real credibility. It is encouraging, though, six years on, that people are still looking and haven't forgotten about Madeleine - that in itself gives us hope.
"There are moments when you despair, but they are infrequent now.
"As someone said: It's not that your burden gets any lighter. It's just that your legs get stronger. That really sums it up."
- Telegraph Group Ltd