Emily Lakdawalla's blog on The Planetary Society has an article on the details of communicating with New Horizons.
Pluto is far away—very far away, more than 30 times Earth's distance from the Sun — so New Horizons' radio signal is weak. Weak signal means low data rates: at the moment, New Horizons can transmit at most 1 kilobit per second. (Note that spacecraft communications are typically measured in bits, not bytes; 1 kilobit is only 125 bytes.) Even at these low data rates, only the Deep Space Network's very largest, 70-meter dishes can detect New Horizons' faint signal.
The article goes into some of the tricks used to improve the data rates and keep within the spacecraft power budgets.
(Score: 2) by Adamsjas on Tuesday February 03 2015, @10:27PM
Well a Collimated beam, of radio or light, might still spread a little, but not to the point we couldn't receive it. There probably isn't much matter to absorb the beam out there in space.
The problem here seems to be the power budget, and storage, and barely adequate transmitters. None of these were adequate to the task of simultaneously snapping photos, and continuous transmission of data.