Hello, This is a long-standing issue, even from Qwitter times.
Steps to repro (approximately, since it's intermittent and really hard to find a scenario):
Launch TwitMonger. Make sure you have an account.
Press Ctrl+Shift+Win+N. Create another account.
Do something within this account, such as post a tweet.
Result: keystrokes are not available anymore, besides Ctrl+Win+arrows. Rest of the key combinations keep silence (JAWS, for instance, just announces, say, Ctrl+Win+L, and TwitMonger does nothing).