Talking about my own experience: You'd hardly win this cat and mouse game in the end.

If someone's goal IS disturbing your site, he would find a way ... using different proxies for example.
Next, you can't rely on someone is entering your site with the same IP all the time anyway. It's quite normal that ISPs shortly drop your internet connection once a day and you'll be back and continue with a different IP afterwards.

Hence, be prepared on doing a lot of manually monitoring until you might find out who is who. In the worst case you have some members who receive their dynamically changing IPs from the same ISP pool - so the bad guy from yesterday may be a good guy today... :)

As Bryce said you have to do via your hosting or server panel.

Further i like to tell you that we are not 24/7 online and when online there are previous tickets to be addressed sending multiple emails will make support more slow. Once we received your email we'll surely reply it and it can take 24 hours at least.

Do you use shared hosting or VPS hosting? This can be done at the server level and block them from hitting your site at all using an IP blacklist. Once you say what kind of hosting it is then it will be easier to direct you