How do I avoid chunks of butter in non-homogenized milk?

I bought a half-gallon of non-homogenized whole milk for something different. I gather that I need to shake it to mix the cream with the milk, but towards the end of the carton (after using it over a week or so), I'm starting to get increasingly large chunks of butter. Is that just the way it is? Am I drinking my non-homogenized milk too slowly?