What if Frederick the Third had fled Copenhagen in 1659? Assuming the Danish remain victorious, the middle class won't ever gain a fanatic love for their king. Although this would be highly uncharacteristic of King Frederick, we can assume an earlier personal POD to result in that. So without this, Denmark has no Revolution of 1660. And no absolute monarchy. How does this affect Denmark in the long run?
It would be bad for his plans of absolutism but might not be catastrophic; Frederick had initiated war and the country had been victorious. The nobility had been decimated during it and would have difficulty in resisting the King.
It would be a bumpy ride but Frederick might still be able to pull it off if only due to the nobility not being able to resist it. The commoners of Copenhagen may still support him as he already pre-war had granted the city nobility privileges and that was something you wouldn't like to lose.
If the country is victorious and King kept from absolute power you probably see a powerstruggle between nobility headed by the sons-in-law of Christian 4 fraction (themselves infighting

) vs. the commoners headed by Copenhagen Mayor.
The country might fall apart with Norway ending up as an independent Kingdom ruled by one of the sons-in-law or perhaps Jørgen Bjelke.
You're probably in need of total defeat or the King losing his nerve like 1658 and a peace dictate like it in order to discredit the King to the public.