If I upload a pdf file to the media library it gets a link like http://myblog.files.wordpress.com/2011/10/myfile.pdf. Is it possible to make a permanent link to it (e.g. the link will not change if I replace myfile.pdf with a new version next month or later). Either http://myblog.files.wordpress.com/something/myfile.pdf or just http://myblog.files.wordpress.com/myfile.pdf would be fine.
It is not possible, you are changing the file, the link has to change.
WordPress creates link based on the date of upload of the file.
What you can do is: use a url-shortner service such as tiny.cc, create a link to redirect to your myfile.pdf and then each time you update your file, you can have the very same tiny.cc link to redirect to your new file.