custom email process not working with automatic checking for emails

Without seeing your code it is hard to tell.

Thanks for answering!
Here is my code:

<?php
/*
Module Name: ReMailer 
Description: Ueber Postie-Plugin empfangene Antwort-EMails werden weitergemailt an urspruenglichen Absender. [Backend]
*/

/* Sicherheitsabfrage */
if ( !class_exists('Toolbox') ) {
	die();
}

/* Ab hier kann's los gehen */
// Siehe Postie-Filter unter https://postieplugin.com/extending/
// postie_post_pre  This filter is called before postie_post_before and before Postie has made any changes.
// postie_post_before  This filter is called just before Postie saves the post. Replaces postie_post.
// postie_post_after  This action is called just after Postie saves the post.
// postie_filter_email 	This filter is called after the "from" email address has been extracted from the email so that you have a chance to change who is the author.
// postie_filter_email2 This filter is called after postie_filter_email and includes the "To" and "Reply-To" fields.
// postie_email_notify_recipients  This filter is called before a success notification is sent and can be used to modify the recipient list.
// postie_email_notify_subject 	This filter is called before a success notification is sent and can be used to modify the subject line.
// postie_email_notify_body This filter is called before a success notification is sent and can be used to modify the message body.

/* Absender und Empfaenger der empfangenen Postie-Mail in custom fields speichern */

function bh_before_save ($post, $headers){
print('<h3>Start Postie</h3>');

print('<u>EMail-Eingang:</u><br />');print_r($post); print('<br />'); print('<br />');

print('<u>$headers:</u><br />');print_r($headers); print('<br />'); print('<br />');

	$absender = $headers['from']['personal'] . ' <' . $headers['from']['mailbox'] . '@' . $headers['from']['host'] . '>' ; 
	$empfaenger = $headers['to'][0]['personal'] . ' <' . $headers['to'][0]['mailbox'] . '@' . $headers['to'][0]['host'] . '>';
	$empfaenger_zielgruppe = substr($headers['to'][0]['mailbox'], 0, strpos($headers['to'][0]['mailbox'],'.'));
	
	$empfaenger_name = substr($headers['to'][0]['personal'], 0, strpos($headers['to'][0]['personal'],' via Aktiv gegen Kinderarbeit'));
	
print('<u>Empf?nger-Zielgruppe:</u><br />');print_r($empfaenger_zielgruppe); print('<br />'); print('<br />');
	$empfaenger_timestamp = substr($headers['to'][0]['mailbox'], strpos($headers['to'][0]['mailbox'],'.')+1);
	
print('<u>Empf?nger-Zeitstempel:</u><br />');print_r($empfaenger_timestamp); print('<br />'); print('<br />');

	$betreff = $headers['subject'];
	$suche = Array('"', 'wpcf7s// ');
	$ersetze = Array("'", "");
	$betreff = str_replace($suche, $ersetze, $betreff);
	
	add_post_meta($post['ID'], 'wpcf7s_posted-empfaenger-zielgruppe', $empfaenger_zielgruppe);
	add_post_meta($post['ID'], 'wpcf7s_posted-empfaenger-name', $empfaenger_name);
	add_post_meta($post['ID'], 'sender', $absender);
	add_post_meta($post['ID'], 'recipient', $empfaenger);
	add_post_meta($post['ID'], 'subject', $betreff);
	add_post_meta($post['ID'], 'wpcf7s_posted-empfaenger-timestamp', $empfaenger_timestamp);
	add_post_meta($post['ID'], 'wpcf7s_posted-text', $post['post_content']);
	
		
	/* ursprünglichen Absender = neuer Empf?nger identifizieren */
	$args = array(
		'posts_per_page'   => 1,
		'meta_key'         => 'wpcf7s_posted-sender-timestamp', 
		'meta_value'       => $empfaenger_timestamp,
		'post_type'        => 'wpcf7s',
		'post_status'      => 'publish,private'
	);
	$posts_array = get_posts( $args );	
	
print('<u>Empf?nger-Nachricht:</u><br />');print_r($posts_array); print('<br />'); print('<br />');
	$empfaenger_postID = $posts_array[0]->ID;
	
print('<u>Empf?nger-Post-ID:</u><br />');print_r($empfaenger_postID); print('<br />'); print('<br />');
	$empfaenger_email = get_post_meta($empfaenger_postID, 'wpcf7s_posted-sender-email', true);
	$empfaenger_name = get_post_meta($empfaenger_postID, 'wpcf7s_posted-sender-name', true);
	$an = $empfaenger_name . ' <' . $empfaenger_email . '>';
	
print('<u>Empf?nger-Email-Adresse:</u><br />');print_r($an); print('<br />');print($an); print('<br />'); print('<br />');

	/* Betreff der weiterzuleitenden EMail definieren */
	$betreff = '' . $betreff;
print('<u>Betreff für Weiterleitung:</u><br />');print_r($betreff); print('<br />'); print('<br />');
	
	/* Weiterzuleitende Nachricht definieren */
	
	$wichtiger_hinweis = get_post(420844);
	
	
	$hinweis_anfang = $wichtiger_hinweis->post_content . "

------------- Anfang der Nachricht -------------
	
	";
	$hinweis_ende = "

------------- Ende der Nachricht -------------
	
	";
	$post_content = strip_tags($post['post_content']);
	
	
	
	$nachricht = $hinweis_anfang . $post_content . $hinweis_ende;
	
print('<u>EMail-Ausgang (Nachricht zur Weiterleitung):</u><br />');print_r($nachricht); print('<br />'); print('<br />');
	
	/* Antworter als neuen Sender mit anonymisierter Mail_Adresse einstellen */
	$sender_name = get_post_meta($empfaenger_postID, 'wpcf7s_posted-empfaenger-name', true);
	$sender_timestamp = microtime(true);
	add_post_meta($post['ID'], 'wpcf7s_posted-sender-timestamp', $sender_timestamp);
	$sender_email = $headers['from']['mailbox'] . '@' . $headers['from']['host'];
	add_post_meta($post['ID'], 'wpcf7s_posted-sender-email', $sender_email);
	switch ($empfaenger_zielgruppe){
		case "kunde": $sender_zielgruppe = "firma"; break;
		case "firma": $sender_zielgruppe = "kunde"; break;
	}
	$sender_email_anonym = $sender_zielgruppe . '.' . $sender_timestamp . '@aktiv-gegen-kinderarbeit.de';
	add_post_meta($post['ID'], 'wpcf7s_posted-sender-email-anonym', $sender_email_anonym); 
	$kopf[] = 'From: ' . $sender_name . ' via Aktiv gegen Kinderarbeit <' . $sender_email_anonym . '>';
	
print('<u>EMail-Header der Weiterleitung:</u><br />');print('<br />'); 

print('Sender-Name: '); print_r($sender_name);print('<br />'); 

print('Sender-Email anonym: '); print_r($sender_email_anonym);print('<br />'); 

print('Kopf: '); print_r($kopf); print('<br />'); print('<br />');

	
	wp_mail($an, $betreff, $nachricht, $kopf);

print('<h3>Ende Postie</h3><hr />');
	return $post;

}
add_filter('postie_post_before', 'bh_before_save', 10, 2); 

Hello Wayne Allen,
Thank you for trying to help.
I have now found the error myself. It was the security query of the plugin through which I call the function. The queried class is of course only present when the mails are retrieved manually …