I have been monitoring the log and do not see any errors related to that task at all. As I stated earlier, the Last start date column is empty, suggesting to me that the task is not even being executed in the first place.
Now that I think of I may not have updated the core plug in when I added this plugin (I have other plugins from you previously installed). Might that have something to do with it?
Yes, you need to use the Core plugin that comes with the Customer Reminders plugin.
Also it might be a good idea to install the Reminders plugin to some local machine and play with them first before installing them on a production server as the plugin sends emails with email templates that I guess you will want to test first.
I would suggest to download the zip package, which contains the very latest version of the plugin and use them.