Haru, as you say that the problem occurs when your members try to change avatars (rather than when they try to upload their first ones):
The way it is supposed to work, is that they can upload a new avatar "on top" of the old one, without deleting the old one first.
But if they delete the old one, then they cannot upload a new one with the same name.
And these options can occasionaly malfunction, for seemingly no reason...
If uploading "on top" of the old avatar gives the error message, then they may need to delete the old avatar first, and then upoad a new one, with a new name.
All this assuming that everything else is done correctly; image size, no spaces in the image name; correct upload path (URL) if you upload from the web, etc.
"Borrow" a user account, or create a test account, and try all options...
FoxLeonard
Edit: deleted option that doesn't exist.