binnn Errors can occur if the atlas file has been edited in some way and does not match the texture atlas page. Unfortunately, I can't figure out the cause of the error just from the screenshots you posted, so if you don't mind, please send us the atlas files that fail to unpack via email: contact@esotericsoftware.com
Please include the URL of this forum thread in the email so we know the context. Then we can take a look at what's wrong.

binnn Thanks! However, the texture atlas page file (the .png file) in the rar file you sent me was corrupted; when I try to open it in Photoshop, etc., it says it is not a PNG file:

I'm not sure whether this is a problem that occurred when you were preparing the file, such as compressing it, or whether this PNG was in this state to begin with and that is why it cannot be unpacked. Can at least this atlas page be previewed on your end? If so, could you just send us the .png file again?