@Andrew +1. Having had spotlight and Alfred mapped to the same shortcut.
I was experiencing this issue as well, but mine is very regular and deterministic. The reproducing flow would be:
1. Typing in App A.
2. Toggle Alfred (option + space), finishing command
3. Dismiss Alfred
4. App A stopped responding to keyboard events (with system beep).
5. Switch to App B using mouse and activate keyboard focus on App B
6. Switch back to App A, keyboard starts working again.
Once I changed those mappings, everything starts working again.