So I was thinking magnets can lose their magnetism due to vibration,temperatue fluctuation and so on. But since pick-ups have magnets and these magnets encouter the aforementioned circumstances, doesn't this mean pick-ups will eventually die or at least lose some of their output amplitude?
yes, but i don't think any of us will be still alive when your pickups die. But it is true they do change their sound after longer periods of time because of that. That's why, when they make some 'vintage sounding pickup', they use processes to emulate natural aging of the magnet to get similar sound as old guitars.