"Download All" fails with "Too many open files"

I have a page with 1500+ attachments. Go to Tools -> Attachments and press "Download All" button beneath the attached files list. The operation fails with this error:

HTTP Status 500 -
type Exception report
message
description The server encountered an internal error () that prevented it from fulfilling this request.
exception
java.io.FileNotFoundException: /home/sven/.../my-attachment.pdf (Too many open files)
java.io.FileOutputStream.open(Native Method)
java.io.FileOutputStream.<init>(FileOutputStream.java:179)
java.io.FileOutputStream.<init>(FileOutputStream.java:131)
com.atlassian.confluence.pages.actions.DownloadAllAttachmentsOnPageAction.execute(DownloadAllAttachmentsOnPageAction.java:41)

When I check the list of open files of Confluence process using 'lsof', I can see a long list of open file handles for attachment files.