A press release from the organisation, which helps vulnerable young people, claims that production company Simco - owned by Simon Cowell - has lodged an application to trademark the name for the show.
Despite apparently pledging to meet up with the charity alongside ITV and Talkback Thames, Simco's lawyers have sent another holding letter as they need more time to consider their position.
Earlier this month, the organisation's chief executive Mark Davyd alleged that X Factor had originally attempted to ignore the issue.
Rhythmix has backed a Facebook campaign for Nirvana's 'Smell Like Teen Spirit' to be this year's Christmas number one.
Brighton rap duo Rizzle Kicks mentioned the controversy on last night's Xtra Factor. Rhythmix has said that it believes producers are under instruction to cover up the story.
> Watch Digital Spy's interview with X Factor group Rhythmix
Watch Rizzle Kicks sneak in a mention of the Rhythmix issue on The Xtra Factor below: