I had a similar issue with the plugin. Lifeinthegrid is probably correct that it is the PHP process timeout issue.
One way to avoid that is if you can afford to leave out the uploads, as those files take the most amount of space (since they are photos and videos etc). This can be done by using the options icon at the top of the duplicator plugin settings screen. By excluding the uploads folder I was able to reduce the package size from 200 MB to 119 MB (the file size of the package can be found out before creating the package by clicking on calculate size link) and create the package.
Let me know if this does not make sense. I will try and upload a video for you for the same.
Meanwhile @lifeinthegrid thank you for the hugely beneficial plugin and now I do not have any butterfly in the stomach when I need to migrate a website from one server to another.