Hi,
Thanks for the post.
From your description, I understand that the finished print jobs do not get removed in print queue and we have to manually delete them.
Please check if the drivers for the problematic printer are certificated for Windows Server 2008 R2. You could check the relevant information from the following link:
http://www.windowsservercatalog.com/
In this case, we could try to delete the problematic printer and relevant driver and reinstall it. After that, please check if this issue will occur when printing the documents on Printer Server.
Hope this helps.