Disable auto-updates for a plugin or theme.
<?php

add_filter( 'auto_update_plugin', 'edd_sample_disable_plugin_autoupdates', 10, 2 );
function edd_sample_disable_plugin_autoupdates( $update, $plugin ) {
	if ( 'my-plugin/my-plugin.php' === $plugin->plugin ) {
		return false;
	}

	return $update;
}

add_filter( 'auto_update_theme', 'edd_sample_disable_theme_autoupdates', 10, 2 );
function edd_sample_disable_theme_autoupdates( $update, $theme ) {
	if ( 'my-theme' === $theme->theme ) {
		return false;
	}

	return $update;
}