When appealing a civil case either side may appeal the verdict as written by uscourts.gov:
Either side may appeal the verdict.
Now I know an apellate court can sometimes deny an appeal. And I know that in criminal trials, if the defendant is not guilty, the court goes a step further and says the government is not even allowed to appeal:
The defendant may appeal a guilty verdict, but the government may not appeal if a defendant is found not guilty. Either side in a criminal case may appeal with respect to the sentence that is imposed after a guilty verdict.
This spurred the following question...
Is there ever a special case where a civil court can legally outright prevent either party from filing an appeal?