I had this issue on my own site, so tested it here and it is the same.
If you check the box to delete your avatar and submit, you end up with a blank avatar in the database (but a default avatar is displayed).
If you then try to add another one, it doesn't work.
You get the "Operation Complete" message, but no avatar.
This is the same whether you upload from your PC, upload from URL, or Link from URL.
The only workaround that we have found is to add an avatar from the gallery, then afterwards add your personal avatar.
Server specs (Server OS / Apache / MySQL / PHP / DragonflyCMS):
Joined: Apr 19, 2004