Around 24 Virgin Galactic passengers have asked Richard Branson for a refund following the crash which killed pilot Michael Alsbury.
Galactic Chief Executive George Whitesides said the news was "unsurprising," but added that the vast majority of customers remained supportive of the project.
Speaking to the Daily Telegraph, he said: "A few people have asked for a refund. I don't think that's surprising and I think what is relevant is that the vast majority have said 'don't give up, keep going, we're with you.'"
Princess Beatrice is one of the high-profile ticket holders who no longer wish to fly, the Daily Mail reports.
A source told the newspaper: "Beatrice was excited by the idea of space tourism, but there is no way she will be going on one of the flights, if they are ever allowed to take place."
Passengers paid £157,000 for a ticket to experience the first space flights, and Angelina Jolie, Kate Winslet and Stephen Hawking are among the 700 people who have reserved seats.
According to The Guardian, Virgin Galactic has collected about £50 million in deposits. With passengers pulling out, the company is expected to lose more than £3 million.
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