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Over time and use it can. The burnt finish is a very thin layer of oxide basically that builds up and makes different colors. The same way a regular metal shift knob will polish up with use it can fade the finish the same way. It will take a lot of use! The colors on it will appear to fade when the oils from your hands touch it for a while but a quick wipe with a damp cloth will remove all finger prints etc to make it look super colorful again.
Unfortunately I don't think there is a burnt finish shift knob that will never fade. Just not possible.