You can challenge it, but not in the way you would challenge most other immigration decisions. There is no appeals board for citizenship, no equivalent of the Immigration Appeals Board (Udlændingenævnet).
The first step is normally to ask the Danish Nationality Office (Indfødsretskontoret) to reopen and reconsider the case.
If you believe the case was handled wrongly rather than simply decided against you, for instance because the reasoning was inadequate or a procedural step was skipped, you can complain about the handling itself. A letter to a member of the Parliamentary Citizenship Committee (Indfødsretsudvalget) is also open to you where the handling of the case looks unfair.
When the ordinary options are exhausted, the case can be put to the Parliamentary Ombudsman (Folketingets Ombudsmand). The Ombudsman cannot grant citizenship. What the Ombudsman can do is assess whether the authorities handled the case correctly and recommend that it be looked at again.
In rare cases turning on a genuine error of law, the matter can go before the courts.
So a refusal is not necessarily final, but the routes are narrow, because Danish citizenship is granted by an act of Parliament rather than by an administrative decision. That is precisely why it is worth having the refusal assessed before choosing which route to take.