Which version of Lightroom are you using?
Ensure that the you have Operating system level permissions for those Folder,specially the Parent Folder
Similar thread Lightroom will not move or rename files!
This can happen if LR is busy doing something with the images in the folder in the background, usually building/checking previews and checking if metadata is up-to-date. It helps if you have Loup instead of Grid view so there are less thumbnails on screen and wait until the little 3-dots symbol is gone on the visible thumbnails.
My guess would be that you do not have Write permission for the folder or the disk that it is situated on.
I am using Lightroom 5. Thanks Akash – I will read the thread you sent!
Eva L. Zahn
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I've been having this problem for years. So much so that after I type in the new folder name, I copy it to the clipboard before committing the change, then when it doesn't work, I can paste it back. Sometimes it will work if I do it again, sometimes it won't work until I start closing open programs, sometimes its IE11, sometimes it's Outlook. Pain in the neck!
I'm running an up to date Windows 8.1 machine with Lightroom CC 2015.5, but this has been happening for the last several versions of Lightroom.