On Mac OS 10.8, latest JUCE, Live 9.0.6 and 9.1.
To reproduce, build the JUCE demo plugin as a 64-bit VST. Put said plugin in Live. Open the plugin window, and click directly on the plugin content to give it focus.
The plugin begins stealing important keys. Neither the musical keyboard keys nor the space bar nor the tab key make it through to Live while the window has focus.
The stealing does not happen until the actual plugin content is clicked on. Just showing the window, or giving the window focus by clicking its title bar, do not cause the problem.
Changing JucePlugin_EditorRequiresKeyboardFocus to 0 does not change the behavior.
The 32-bit and AU plugins do not have the problem.
This problem was reported with the last update of my plugin in February of this year, so it's not a brand new thing.
I found a topic here: http://www.juce.com/forum/topic/keyboard-handling-live-os-x-108 reporting the same problem, that did not receive any attention at the time. The poster has a workaround of forcibly losing the window focus. It works for me, but it's not really a good solution.