Line 307 of plugins/download-manager/admin/menus/class.Settings.php reads
$purchased_items = remote_get('https://www.wpdownloadmanager.com/?wpdmppaction=getpurchaseditems&wpdm_access_token=' . wpdm_access_token());
If you change this to
$purchased_items = wpdm_remote_get('https://www.wpdownloadmanager.com/?wpdmppaction=getpurchaseditems&wpdm_access_token=' . wpdm_access_token());
It works.