Hi! Thanks Alexandre and Amos for your replies, together they pointed me into the right direction!
Based on the the URLs sent by Alexandre, I edited the "/etc/php5/cli/php.ini" file and tested different values for "max_execution_time" and "max_input_time" but none changed the PHP's script behavior. Then, I remembered Amos mentioned a 60sec timeout. I saw my cache.log and yes there was an exactly 60sec delay after starting squid and the first Warning. So, I searched the "php.ini" for a similar value and found this directive: "default_socket_timeout". I changed it to 300sec and the Warnings started to show up accordingly. Then I changed it's value to "-1" and the warnings haven't shown up again! Squid doesn't complain anymore about my PHP-scripts, but I don't know if this change has secondary effects or any other consequences. I'll be monitoring them, but in any case I have the backup Perl-scripts. Thanks again!
