Why does the New Horizons probe to Pluto have such as short operational window?

When New Horizons reaches Pluto in 2015 it will only study it for a few months. Why is the encounter so short? Why, like the Cini probe, can't it stay in orbit for a few years to really study it in depth? After all, this is likely to be the only study of Pluto for some time, possibly in our life time.