Olympic medallist Amy Tinkler says she has "no confidence" in British Gymnastics' integrity unit's "ability to be honest and moral".
Tinkler, 20, says she has not received an explanation as to why her formal complaint was dismissed last month.
She submitted a complaint over allegations of mistreatment within the sport in December 2019.
In an open letter to integrity director Richard Evans, she asked what it is "going to do to improve".
On Wednesday, Tinkler said in a separate open letter to chief executive Jane Allen that British Gymnastics is "prolonging her suffering" by failing to give an explanation as to why her complaint was dismissed.
Eighteen minutes after posting the letter on Twitter, she received a reply from Evans proposing a meeting to "discuss her concerns".
In a response on Thursday, Tinkler questioned why it was Evans responding, and not Allen.
"I hope you understand how frustrating it is that you only reply when publicly prompted," she said.
"My letter and questions within it were addressed to Jane Allen and I hope she answers them within the timeframe. I think I deserve that. I've been told that's what a CEO should do."
She added: "My preference isn't to have this conversation in public, however after 272 days of waiting I have no confidence in your department's ability to be honest, moral and deliver an outcome in private.
"Do you understand that? What are you going to do to improve?"
BBC Sport has contacted British Gymnastics for comment.
Part of Tinkler's complaint related to her "experiences" with national coach Amanda Reddin, who has temporarily stepped aside while an investigation into claims about her conduct takes place. She has denied any wrongdoing.
Tinkler says she has emailed British Gymnastics three times "asking for an explanation or summary outcome" without reply and discovered "via a third party" on 10 August her complaint had been closed.
Tinkler, from County Durham, was Great Britain's youngest medallist at Rio 2016, when she won bronze aged 16, and also won one world medal, three European medals and 10 British titles during her career.
In July, British Gymnastics announced an independent review would take place and Allen has said the organisation had "fallen short" in protecting its members.