The first thing that comes to mind is that your WordPress settings for how to display dates is messed up, since my plugin uses that setting to determine how you want dates displayed on your site (to be consistent, and since different countries display dates in different ways).
So, you may want to check that setting first. Go to your admin dashboard, under Settings>General, and then scroll down to date format. If the “custom” box is selected, but there are no date format characters in the input, then dates will not show.
If that’s not the problem, then I’m not sure what would be happening, and you would need to start a process of elimination by switching themes temporarily to see if it’s a theme issue, and, if not, switching off other plugins one at a time to see if the problem goes away. If some other plugin, or the theme, is tapping into one of my hooks, or into the WordPress date display option hook, or somehow messing up the dates in the database table, there could be a conflict, but that would be a strange one.