WordPress custom post types do not alway support comments. Look at the Screen Options tab on the new_post page for your custom post type. If there is a ‘Discussion’ checkbox, make sure that it is checked. After checking it, find the Discussion meta box (it should be underneath the editor) and then check Allow Comments.
If you don’t see a Discussion checkbox in the Screen Options area, then the custom post type doesn’t support comments. If that’s the case, you will need to contact the plugin’s author to see about getting comments enabled.
If the plugin is available in the WordPress repo, I can try it out.