For me, the trouble was in class.mailfetch.php. About line 300 appears
$sql=' SELECT email_id,mail_host,mail_port,mail_protocol,mail_encryption,mail_delete,mail_errors,userid,userpass FROM '.EMAIL_TABLE.
' WHERE mail_active=1 AND (mail_errors<='.$MAX_ERRORS.' OR (TIME_TO_SEC(TIMEDIFF(NOW(),mail_lasterror))>5*60) )'.
' AND (<STRONG><s>**</s>mail_lastfetch=0<e>**</e></STRONG> OR TIME_TO_SEC(TIMEDIFF(NOW(),mail_lastfetch))>mail_fetchfreq*60) ';
Change to
$sql=' SELECT email_id,mail_host,mail_port,mail_protocol,mail_encryption,mail_delete,mail_errors,userid,userpass FROM '.EMAIL_TABLE.
' WHERE mail_active=1 AND (mail_errors<='.$MAX_ERRORS.' OR (TIME_TO_SEC(TIMEDIFF(NOW(),mail_lasterror))>5*60) )'.
' AND (<STRONG><s>**</s>mail_lastfetch Is NULL<e>**</e></STRONG> OR TIME_TO_SEC(TIMEDIFF(NOW(),mail_lastfetch))>mail_fetchfreq*60) ';