The people who host your site on their servers DO have the ability to block
specific/range off IP addresses if they can be arsed to do it.

Also, sharing someone elses server is not that secure IMO.

I too have had similar hacking "attempts" and am in the process of hosting my
own site on my own server. This means I will have total control on access rights.
(Plus a few other benefits )

It is not that expensive to set this up but does require a reasonable level of
network IT skills so it is not really a DIY type job for most.
Price depends on equipment quality and bandwidth.