The original had the same issue, but there is a fix for that, it pretty much replaces the stick with a thumbstick from a gamecube, like this one:
https://www.amazon.com/Redesigned-REPLACEMENT-Joystick-Controller-Thumbstick/dp/B009MRZAUC/ref=sr_1_1?ie=UTF8&qid=1508806910&sr=8-1&keywords=n64+controller+thumbstick