It seems this is happening on your shared site because the theme code that you are using is conflicting with plugin code. Yo can test the plugin with any default WordPress theme to see it is working fine.
You can try resolving the issue using this small custom plugin https://drive.google.com/file/d/1KqnuvWWrXfTqYETkMR62XipRDWR5NkNJ/view?usp=sharing on your site that contains following code.
function add_custom_scripts(){ ?>
<script type="text/javascript">
jQuery(document).ready(function($){
$('.search-close').click( function() {
if ( $( '.astm-search-menu' ).hasClass( 'open' ) ) {
$( '.astm-search-menu form' ).animate(
{ width: '0' },
400,
function() {
$( '.astm-search-menu' ).removeClass( 'active-search' );
$( '.astm-search-menu' ).removeClass( 'open' );
}
);
} else if ( $( '.astm-search-menu' ).hasClass( 'dropdown' ) ) {
$( '.astm-search-menu form' ).fadeOut();
}
});
});
</script>
<?php }
add_action('wp_footer', 'add_custom_scripts', 99);