Like so often before, the devil is in the details.
While I have no major principal objections to copyright infringers being kicked off internet (if they use internet for the infringement), I would want to know more of the details before making my mind up.
For starters, I would want everybody to be given a fair trial, and only when they have been found guilty three times should they be kicked off internet. I get the impression that with the present suggestion it's enough to be accused of copyright infringement three times to be kicked off. That is taking other people's right too easily: it should require a trial according to the country's requirements.
Secondly, I think there should be a time limit to how long you are banned from internet. I see no reason why a mere copyright infringer should be banned from internet for life. It's not like you can use copyright infringement to kill someone...
Thirdly, I would like to know what provisions the law provides to protect the technically challenged. Suppose my neighbour hacks into my WLAN, and starts sharing files. I suppose the recording industry would like to hold me responsible, but should they be able to do so? In my opinion, no. Granted, the recording industry will not like the "I am an idiot with technology"-defence, but this kind of trial should be held to the same standards as all others: the accused are presumed innocent until proven guilty beyond a reasonable (or similar) doubt.
Fourthly, what of family members? Suppose I get kicked off internet for copyright infringement. What of my wife and my children? As far as I know, no modern democracy allows collective punishment, so it should be acceptable for my wife and children to get internet access at home. So why then bother with banning me, if the effect is that the internet connection is simply passed to my wife?
For an interesting comparison, move the "getting banned from internet for copyright infringement" to the world of printed matter: any person or company thrice accused of copyright infringement gets banned (for a short period of time, eg a year) from reading and writing. The effects would be quite devastating... You would have to have somebody read the bus timetable to you, you would have to have somebody write your checks for you, you would have to have somebody read your letters to you... And if a newspaper were accused of infringing someone's copyright three times, they could obviously not print a single letter the next year!