Styli have a lot of work to do:
On an average 12" record, the stylus moves over 500m through the groove on the record. So over time, it really has a long way to go! Over many records, the tip of the stylus does wear down, but it's hard to know at what point the stylus should be replaced.
It will depend on the type of stylus you use and how well you look after the stylus but according to Ortofon:
"With proper care we find that up to 1000 hours is possible without degradation of performance. The stylus does begin to exhibit changes after 1.000 hours, but the stylus life as a whole is expected to top 2.000 hours." - Ortofon
When the stylus begins to wear down, it is very possible for it to cause damage to your records. It can do irreversible damage to the high frequencies on your records.
So how do you look after your stylus?
It's also worth noting that some stylus types (such as spherical styli) can damage your records a lot more quickly. It's easy to replace a stylus, but it's not always easy to replace your vinyl!