Hi!
It looks like there may be a conflict with another theme or plugin. Can you try deactivating all other plugins, ensuring The Events Calendar and Events Calendar PRO are up-to-date and then switch to a default, unmodified theme such as Twenty Twelve?
If the problem disappears under those conditions, ie search works as expected, then reactivate everything one component at a time, checking at each stage to see if the problem has returned.
This should help to isolate which if any component is interfering – we can then take things from there.
Thanks!