With respect to the data being entered onto the time entry notes, are you aware of the data being entered, with respect to number of characters etc.
As per the details you had provided, it seems like the feature is working for other users ?
As suggested above, definitely look into the app-ca log. In case if you do not observe related entries on it, you may also enable an action trace on the user's profile and ask the user to carry out the same steps and then check the trace data.
Action Trace:
You can setup an action trace based upon the following guidelines:
Using PPM Action Trace
Let us know how it goes.
Regards,
Samik