I'm not sure any musical instruments do have an infinite life.
None of the fragile stringed instruments such as lutes, theorbos etc last a long time. Guitars require regular tweaking, refretting, neck re-alignemnt etc.
Top quality violins appear to last for ever, but in reality they are carefully maintained and suffer from cracking and changes in table arch just like any other instrument. I've even heard that violins are routinely taken apart to restore the arch etc, though I don't know how true this is.
Woodwind instruments suffer all sorts of problems.
Pianos have a limitied life. Some people say as little as 25 years before they've lost too much of their tonal quality, and as a pianist I have to go along with this (I'm thinking of having my mother's 100-year old Bechstein upright fully restored, as it's such as nice instrument, but we're talking of a TOTAL rebuild). Harpsicords etc are relatively fragile.
Church organs need voicing and even tuning every so often
Harmoniums suffer all sorts of problems (I'm restoring one at the moment).
A friend who makes handmade gongs and cymbals talks of them loosing their tonal qualities after a certain time.