Depending on your state’s laws, a court can dismiss or deny your divorce for failure to meet certain requirements, but it won’t deny your divorce simply because one spouse does not want it (at least that is accurate for states with no fault divorce, like Connecticut).
Most states have some prerequisites and procedural rules that must be followed for a divorce to be properly brought before the court and followed through to judgment.
The court could deny to grant your divorce if you fail to properly serve your spouse with the requisite divorce papers and that spouse does not appear in the action, for example. In that situation, you would need to correct your service issue before a court can grant you a divorce.
If you fail to comply with local court rules regarding filing of required documents by certain deadlines, especially those required by your case management date (ie. a parenting plan, financial affidavits, case management agreement regarding scheduling deadlines), then a court could dismiss your action if you are found to not be in compliance or not in court that day (see: Connecticut Judicial Branch Superior Court Family Matters Standing Orders ).
When a divorce is dismissed or denied, the court will usually dismiss/deny it “without prejudice.” If this is the case, the court isn’t saying that you can never be granted a divorce. Rather the court is saying that the current case is terminated, but you are free to start over and file for divorce again.