I don't think this is true (that people get bored and need change). People get used to the way the website looks and no longer pay attention, plus they know exactly how everything works so a change is indeed disruptive (we've all been there, moaning that they've changed the way it worked!)

BUT, this is a relative thing. New shiny apps and websites will appear and suddenly yours looks dated and crp and so you become under pressure to update it.

You nailed it, though: "Please don't overdo re-designs just for the sake of it.*"