Both of our apartments are Bopælspligt and as you we rent them both out very successfully.
I believe that if the board were to make such a rule, all owners would have to vote and approve it. I don’t believe they can just implement the rule themselves.
You therefore need to persuade your fellow owners to vote against it.
As you know property prices in Copenhagen are flying upwards at the moment, especially so for property without residential status. We are constantly on the look for another such property at the right price. The real estate agents we’re working with tell us that such properties are currently commanding a 15-20% premium, with many people looking for Airbnb investment properties. Any embargo on the number of nights you can Airbnb would have a serious impact on this premium - people don’t like to see there properties devalued so this could be a very compelling argument.