I found a solution that works for my website. Your mileage may vary.
The version of Events Maker my website uses came bundled with the theme. The theme includes some templates for events. I discovered that in the Events Maker settings, under the templates tab, there is an option to enable the use of default templates. I unchecked the box for using default templates, so Events Maker uses the templates included in the theme. That fixed the empty calendar problem for my website. It seems that the Events Maker default templates are buggy.