I guess it only re-evaluates the PID values every 60 seconds now
Exactly.
but the flap still moves from open to close within 2 seconds
That doesn't seem contrary to requirements.
However my control process is very slow so I want to change the flap position only every 60 seconds (maximum movement 10 degrees per loop).
I guess the most obvious question is why you need PID for this, then.
The second most obvious question might be "Where's your code?".