Difficulty will keep going up forever but at a slower pace. I believe we would see a drop when after the bitcoin halving..
That isn't actually true according to what I have read. It fluctuates according to how many blocks are found at a given speed. So if blocks are not being found fast enough, the difficulty will actually decrease to make it so that blocks are found more easily, I believe the time they try is every 10 minutes, someone can please correct me if I am wrong though.