Now 73, Williams has been quadriplegic and in a wheelchair since a road accident in southern France in 1986. The Briton spent some time in hospital last year for treatment to a pressure sore.
"Frank is team principal. Always has been and always will be until we find him one day face down on the desk," said Claire, the deputy team principal.
"Frank is in there 24/7, he's in the office more than any of us. He loves it, he's passionate about it but he has a management team in place that he trusts to run the business," she added.
"But Frank is there, he will always be and has no plans to retire. It wouldn't be the same without him."
Williams, winners of nine constructors' and seven drivers' titles between 1980 and 1997, are fighting their way back to the top after a decade of decline and finished third overall last season.
They are currently third after four races this season, behind champions Mercedes and Ferrari who operate on significantly greater budgets.
Frank Williams still attends races, although not all, and keeps a close eye on business dealings and sponsorship even if Claire has taken on more such responsibility.
She said improved performance on the track had led to an increase in the team's rate card although Williams remained more flexible than some rivals.
She denied however that they had undersold themselves to attract partners at a time when all teams are struggling to secure sponsorship and some are fighting to survive.
"We are more flexible in our approach than certain other teams, but that's not to say that we ever undersell ourselves," she said.
"There's commentary that (title sponsor) Martini may have been undersold. Well, no. Not at all. We can't do that because we can't afford to do that."
Claire said some partnerships had also moved away from visibility on the car and were increasingly focussed on other elements such as advanced engineering projects, 'thought leadership' and education.
"You can look at a Manor (car) and it's got nothing on it. And you could say 'the health of Formula One is on the wane.' But actually, what else are we all doing behind the scenes?," she asked.
(Editing by Amlan Chakraborty)
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