Please make sure that you have installed the latest version of IDM. Old versions before 6.09 build 3 have a bug with processing of cookies and may not work with sharing sites.
Please note that you SHOULD NOT press "Logout" in ANY browser. Otherwise, cookies will be changed.
Problem may happen if you use some proxy. It is better if you not use any proxy at all. If you absolutely cannot avoid using proxy, you should use the same proxy in your browser and in IDM. Otherwise, the site will think that you use different IPs for this download and download will fail because a temporary link can be downloaded only once from a single IP address. Please note that the same relates to different applications that try to control your internet traffic and acts like local proxy. It can be some kind of FireWall/Antivirus or other security applications. If you use your browser via such application, you should use IDM via it as well.