An IP address is not a unique identifier. It should almost never, alone, be used to identify a specific visitor. It may be combined with some other variables to temporarily deter access, however other people may share the IP address at the same time (like on a college campus, or a cafe), or may be assigned that address later (typical ISP behavior).
The best part is, anyone can just use a proxy if their IP address is blocked, and there is nothing you can do to stop them.
What you should do is come up with a way to prevent whatever the person is doing to warrant a ban in the first place.
That isn't to say there aren't times when banning entire network blocks is a perfectly reasonable action, but it should definitely be done sparingly, not out of laziness.
Have you tried turning it off and on again?