Losing parties are always entitled to appeal the final decision of a Federal trial court.
Parties usually cannot appeal before a final decision, although there are several exceptions. For example, there may be an "interlocutory" appeal if both the United States District Judge certifies that a decision by the Court of Appeals could expedite the case and the Court of Appeals agrees to hear the appeal before a final judgment is rendered. (This might happen if there is one critical legal issue that would determine the outcome of an important case that would otherwise take months to present at trial.) Injunctions are usually appealable before a final judgment, and there are a few other types of decisions that are immediately appealable, such as contempt orders.