I have a similar problem with one user. It was reported as a Notes "crash". It turned out that the keyboard becomes unresponsive but only in Notes. Trackpad works fine. It was reported as resulting from searching within mail which I did confirm that I could reproduce on this Macbook Pro. After a few searches, the keyboard no longer produces input.
The machine is running Notes 9.0.1 on OSX 10.11.3. I could not reproduce this on another Mac (Mini) running the same Notes and OS versions.
The unresponsiveness was both with the built-in and wireless keyboards and occurred with and without bluetooth on. This users has as a TON of other apps installed. My test Mac has virtually nothing else. That's all I have to go on so far.