Hi Elma!
Thanks for reaching out to us! Let me help you troubleshoot this issue.
Having a closer inspection at your site I can see there is a Javascript error that triggers when trying to use the search.
First, please make sure you update to the latest versions of our plugins. Remember you can always download the latest versions by going to your downloads page > https://theeventscalendar.com/my-account/downloads/.
I also noticed you are using an older version of WordPress (4.4.11), so please update to the latest version.
We always suggest to setup a dev/staging site so you can test things out and make all plugins, theme and WordPress core updates without disrupting the live site.
After updating the plugins and WordPress core, do you still experience the issue? Let us know.
Thanks,
Victor