Provincial Supreme Court Judge Gillian Butler ruled last week that Cabana had failed to establish a reasonable belief that she is biased.
Cabana had asked that Butler remove herself from the case because she's married to a partner in a law firm that's representing former premier Danny Williams.
Williams is involved in a defamation lawsuit and countersuit with Cabana.
Cabana argued that if he loses the Muskrat Falls challenge, any court costs imposed against him would limit his ability to fight the defamation case.
He is trying to stop the $7.7 billion hydro project in Labrador, alleging constitutional violations and legal uncertainties.
Cabana says he won't appeal at this stage for strategic reasons, and that no new court dates have been set for his challenge to proceed.