Problem with reply to automatic email sent module

Hi,
I have a new problem with reply email but in version 3.4.4. Reply mail are not added in "Notes"
I did not change my configuration that worked in 3.4.1. Here are the logs (with your debbug Cron.php) ... I confess I do not understand the problem.

2013-08-20 13:18:21 ..... SCRIPT .... 90.85.53.162 Cron::checkEmails()
2013-08-20 13:18:21 ..... SCRIPT .... 90.85.53.162 Cron::init()
2013-08-20 13:18:21

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DEBUG

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Cron::checkEmails() - Step 1
2013-08-20 13:18:21

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DEBUG

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Cron::checkEmails() - Step 2
2013-08-20 13:18:21

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DEBUG

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Cron::checkEmails() - Step 3
2013-08-20 13:18:21

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DEBUG

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Cron::checkEmails() - Step 4
2013-08-20 13:18:23

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DEBUG

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Cron::checkEmails() - Step 5
2013-08-20 13:18:23 ..... SCRIPT .... 90.85.53.162 Cron::getCheckEmails()

Thank for your help

Nothing to do, I have already tried your suggestion. I even reinstalled the files but I can not identify the problem without further log on gmail imap server connection that I check reply mail.
Regarding the Cron.php in trace mode I just picked up the file you provided earlier in this topic

Other idea ?

yes every 30 seconds. No other trace. I test mailbox in gmail for account and pwd and with other mail client ... all is ok. I check and recheck global parameter ... all ok ... arghh !