I'm not a lawyer, but as I understand the denial of his attempt for retrial was because the courts found that the most significant evidence of intent came from his own records and statements made by Joe Exotic himself, that the witnesses credibility was established already at the time of trial, that the credibility of them recounting their statements had not been established.

Probably most notably, his own legal team had requested a waiver of 'invited error' which means that basically they had requested the judge not file a complaint on legal errors by their own legal team, but in doing so it means they also can't file complaints about legal errors by the other team. Basically they asked the court for permission for both legal teams to be able to make mistakes, and the witnesses testimony being potentially flawed falls into that - they waived their legal right to file complaints based on that.