The phrase "despite refusing" is grammatically correct and can be used in written English.
It is typically used to introduce a contrast or contradiction between the action of refusing and another event or circumstance. It can also imply that the refusal did not prevent the other event from occurring. Example: Despite refusing to apologize, Sarah's friends still forgave her for her mistake.
But Kroenke is on the board despite refusing to sign the lock-down.
It's not easy to tell if, despite refusing to be interviewed on camera, they gave Morley off-the-record guidance.
He has not worked since, despite refusing to spend daytime hours at home and engaging in a permanent job hunt.
Last week, high-street rival Next recorded its best Christmas results since before the recession despite refusing to begin discounting before Boxing Day.
Mourinho had aimed fired at Wenger before the weekend, despite refusing to mention him by name, by suggesting he was an exception to pressure managers are under.
Sherborne complained that Thurlbeck had protested his innocence on Radio 4 despite refusing to answer questions about hacking when he appeared before Leveson.
The foreign minister, Louis Michel, called the decision to sell arms to Nepal eminently ethical", despite Germany refusing to follow suit.
All eight of the band's albums now appear on Spotify, Deezer and Rdio, despite previously refusing to allow streaming services to access their work.
In fact, despite politely refusing to meet in his apartment ("Many of my close friends have never been invited into it"), Shawn couldn't be more courteous.
Despite MPs refusing to give prisoners voting rights, Clarke said he thought the government would have to go along with the ruling: "We have got to have a look at how we comply with the law".
Despite initially refusing to give evidence to MPs, Ashley appeared before the committee in June and admitted his company had broken the law by failing to pay staff the national minimum wage.
