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I'm dealing with this in my Arduino HOTAS software now, polling the encoder even hundreds of times per second you'll miss steps from quick turns, like you are seeing now. The other way is to use interrupts, which interrupt your program the moment a change is detected on the pin but then you get the problem that it's too fast and you'll detect the bouncing of the switches. That's fixable on the hardware side with a filtering circuit or possibly from coding in a short lockout so that changes with x microseconds are ignored.
You should be able to drop in this library and be up and running pretty quickly if you don't want to try and write the code yourself.
Keep an eye on this repo as it'll be updated with the encoder functionality in the next couple of days.