it sort of depends on how you're rendering, actually. If all you have is a JFrame rendering with a BufferStrategy from that JFrame, then the JFrame needs to be handling the events (and the JFrame is likely the only AWTEvent-capable container you're using in that situation)
If your fullscreen frame is using a panel or some other container, it might not have focus (the fullscreen may have it). a few ways you can fix this:
1) allow the fullscreen window to pass events to your container
or
2) use the setFocusable(false) on your container, and do all event handling with the frame
but most important of all: post your code, so I can stop taking guesses at what the situation is
