I use this patch to allow search by date only:
hajma@debian:~$ diff /var/lib/wordpress/wp-content/plugins/another-events-calendar/public/class-aec-public-search.php.bak /var/lib/wordpress/wp-content/plugins/another-events-calendar/public/class-aec-public-search.php
44c44
< if( ! $search_query ) return __( 'Sorry, no results matched your criteria.', 'another-events-calendar' );
---
> //if( ! $search_query ) return __( 'Sorry, no results matched your criteria.', 'another-events-calendar' );
hajma@debian:~$ diff /var/lib/wordpress/wp-content/plugins/another-events-calendar/widgets/search/views/widget.php.bak /var/lib/wordpress/wp-content/plugins/another-events-calendar/widgets/search/views/widget.php
16c16
< <input type="text" name="aec" class="form-control" placeholder="<?php _e( 'Search by event title, desc...', 'another-events-calendar' ); ?>" value="<?php echo isset( $_GET ) ? sanitize_text_field( $_GET ) : ''; ?>" required />
---
> <input type="text" name="aec" class="form-control" placeholder="<?php _e( 'Search by event title, desc...', 'another-events-calendar' ); ?>" value="<?php echo isset( $_GET ) ? sanitize_text_field( $_GET ) : ''; ?>" />