Depends. Depends on why you had arthroscopy to start with. Uncomplicated meniscal tears usual improve in 2-6 weeks. If there is arthritis present the pain may never completely resolve. For more involved arthroscopic procedures it is anyone's quess as to how long the pain may persists. Your surgeon is the best one to advise in this matter.
Postop knee pain. The knee pain should be worked up to include but not excluded to same sided hip pain and lower back pain; specific to the knee quadriceps eccentric weakness can be a common cause for persisting knee pain; an MRI is needed to look for a residual bakers/popliteal cyst; evaluate for any subchondral bone marrow edema or insufficiency fracture and possible re tear of a meniscus.