Same diagnosis really. Indeed it probably reinforces it -- some crud, corrosion, wear... on the track inside the stick. Pushing it in probably dodges this enough to work again. Outside chance of a cold or cracked solder joint where the stick assembly meets the board and the pressure makes it work but 99 times out of 100 for me then it is crud in the tracks for every controller I have ever pulled part on any system, and where it is said solder problem it is usually a failure in the design or a decade or more on from its release. For car electric window switches then that rises a bit to more like 80 times of 100 that it is crud but that is a different discussion.
Pull it apart and clean it if you can, else replace the stick assembly.