If the parent takes an initial interest as well (as in, they WILL read the notebook to see what their kid must practice, and they are aware of what must be accomplished the first few weeks), then the child tends to get along their way quicker. The students whose parents don't give a crap end up being blindly forced into taking lessons because "it's good for them"... the parents with that mentality bug me, and probably are the types of parents who ground their kids for getting a C on a test but won't help them with their homework.
I've lost several students after 2-3 years, and for those who weren't due to a reason like moving, financial, etc, they all had parents who didn't give a crap about how their child was progressing. If a kid can get away without doing ANY homework at school, bomb test after test and just scrape by while their parent does nothing to change it, the kid can surely do the same with piano. The difference is, an 8 year old can't 'quit' school.