I’ve got the same problem here: it has nothing to do with the server or the hoster because nothing changed but the WordPress 3.6 update. Since then your plugin does not work anymore.
I get the 0kb problem on two different servers, completely different, except for WordPress 3.6. Switching back to 3.5.4 solves the problem.
So your plugin is not WordPress 3.6 compatible and as we need a working download manager, could you please inform us if there’s going to be an update soon (the update today did not solve the problem) or not. If not, we can look for a different plugin.
Thank you very much!