According to the post:

$ netstat -an | grep -c TIME_WAIT

If the count it returns keeps growing, you're seeing a slow leak. At some point, new connections will start failing. How soon depends entirely on how quickly your machine closes new connections.

Since a lot of client traffic involves the server closing connections instead, I imagine it could take a while.

It's unclear if it'll leak whenever your mac closes or only when it fails to get a (FIN, ACK) back from the peer so the TCP_WAIT garbage collector runs. If it's the latter, then it could take substantially longer, depending on connection quality.