Lifespan of a bike child seat
Barring damage from sunlight or collision, or fabrics rotting from dampness, or abraiding, a child's seat should be usable for decades.

I'd strongly recommend including the child's seat in your periodic M check.  Wiggle it, lift and push on it, look for changes or cracks.  Tug on the belts and make sure nothing's loose.

Store it according to instructions, wash the cloth parts as required and dry them before storage, and you should be okay for an entire generation, and probably the next as well.



Aside - one neat historical record can be to write the child's name and birthdate on the seat in a place where it won't rub off.   I've seen one kids seat with a dozen names on it going back to the late 80s.