Adrian Peterson Judge -- I Ain't Goin' Nowhere

Prosecutors in the Adrian Peterson child abuse case have a tough fight ahead of them ... they tried to 86 the judge for trashing them ... and they just failed.

Another judge has ruled ... Judge Kelly Case will continue to preside in the trial ... even after calling the district attorney and Adrian's attorney "media whores."

TMZ broke the story ... the D.A. demanded and got an apology from the judge ... but they wanted more -- they wanted him off the case. Judge Case wouldn't budge, so prosecutors went to the wall with another judging ... claiming Case harbors a personal grudge against the D.A.

The second judge said prosecutors must show compelling evidence that Case is biased ... and they failed.

So Case is still on the case.