When using multiple monitors, and the primary is not to the left, Snipping Tool will only allow capture from one monitor.
I have a laptop display that is my primary, and a second monitor extended that is above the laptop display. To configure this, in the 'Screen Resolution' applet, simply drag the second monitor (2) above the primary (1) and hit apply. The snipping tool will no longer work on the second screen.
If you move (2) to the right, hit apply, open Snipping Tool, and move (2) back to the top and hit apply (with Snipping Tool still running), the tool can capture from either display.