I would actually argue against this.
User annotations should, as a rule of thumb, be immutable.
If they can be edited, then they can be changed after the fact such that they no longer reflect the situation at the time. Yes, this can be worked around by having a history of revisions, but that's further complexity.
Since user annotations are only visible to a very small subset of users, and should be used relatively sparingly, it doesn't seem an unreasonable burden to just add a second annotation to amend the previous one if the need arises. A clear indication could also be added, something like "(replaces 12:02 Z)" or "(amends 23:59 Z, premature save)" at the beginning; this would indicate to those who see it that the new one supersedes or amends the earlier annotation.