Don't take yourself so seriously.
When a student like this leaves, we feel responsible, however the bad feelings are usually not without warrant.
Some students bounce from place to place complaining about teachers, but, "If there is a funny smell where ever you go, check to sole of you shoe".
Your reputation matters very little in these circumstance, providing you are who you say you are.
If you do what you do, to a high quality, with good students, and evidence of good students and teaching, people will gravitate towards you.
Generally speaking, the people who gossip are not the sorts of client you want.
Please get over it; its not as bad as you think or feel.
Was that your first?