So, my game was constantly running at a 60 fps but every now and then it started to have some really strange framerate spikes which occurred ~3-5 minutes after running the game in Xcode with a physical device. I couldn't narrow the problem down with Xcode's instruments, so I started to remove huge chunks of various parts in my codebase. And then, after 2 days (!) of fiddling around and being on the brink of insanity I finally found out that Xcode's GPU Frame Capture setting was causing this.
So if you are wondering why your game is running badly but cocos2d still displays continuous 60 fps, try to disable this "feature":