Are you making sure you wait long enough for Cachly to send the update to geocaching.com? Meaning, if you delete the note, then return to the details screen and update the cache quickly, it is likely that the note had not been updated yet on geocaching.com, so you would get the note before the update.
Also, can you let me know why you are quickly updating the cache after clearing the note? It wouldn't require an update to the cache, so just wanted to check if you were needing to do that for another reason.