If you start a download and it completes without actually downloading any files, the support module for the site is probably outdated. If you report the site as not-working (along with an example URL or two), it will be fixed in one of the following updates.
Sometimes you might see “Completed (Some failed)” in the status column. This means the program detected that there were files that weren’t downloaded properly. To see a list of failed files, check “Create a text file listing missing/failed pages” under “Settings > Save to > Metadata”. This will generate a “failed.txt” file in the manga directory after an attempted download, which contains a list of the failed files. If you’re reporting a bug, it can be helpful to include this file with your bug report.
It may also be working checking that it is not a firewall or ISP block that is preventing the program from downloading the files. You can find a detailed list of these types of problems here.