its not broken...
it happens over time. you more you play the more loose it gets. the only way to aviod this is to not play that much.
you can also avoid this by playing with the D-pad as much as you can.
and a possible repair method costs about $20... buying a new controller.
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or you could just pry your joy stick out with a screw driver, try to add some more things to the platstic holder to add the same movment. and some how get the joy stick back in without messing anything up