Hi Jennifer,
I had a simular problem a few weeks ago, it would let me remove a resource link from the course page but when I tried to delete it in the files area the file just wouldn't go away. The reason behind this I discovered was that the file name contained an apostraphy (') and for some reason Moodle didn't like it so the only way I could delete it completly was to delete the file from the server.
I hope this helps,