My SharePoint 2010 Farm has 2 WFEs and 1 APP server. The APP server was hosting Service application and the index and crawl components split between web front ends.

I encountered the following error

catalog Main: failing to copy index files from crawl component 4 for <x> minutes. Access is denied

So, digging further did not result in finding any suitable fixes.

So, I created a new query component folder, mapped the new folder to the Query component and removed the old folder reference.

 Navigate to Search Administration (Manage service applications - Select Search Service Application). Modify Topology - Pick the query component causing the issue and edit properties

Try the above approach and if still does not work, do an index reset (watch out... if you are indexing a lot of content... this may take a long time to index the content back again) along with a new folder mapping. I did not have to delete the Query component and re-create it.

Happy Searching!