Logrotate: how to access the output file in postrotate

Ok, it seems that it has nothing to do with logrotate. I think the errors you see are from fail2ban which is looking for these files. Try tu run manually the postscript from fail2ban in /etc/logrotate.d/fail2ban (o something like that) and you will see the errors.

man logrotate

   dateformat format_string
          Specify  the  extension for dateext using the notation similar to strftime(3) function. Only %Y %m
          %d and %s specifiers are allowed.  The default value is -%Y%m%d. Note that also the character sep‐
          arating log name from the extension is part of the dateformat string. The system clock must be set
          past Sep 9th 2001 for %s to work correctly.  Note that the datestamps  generated  by  this  format
          must be lexically sortable (i.e., first the year, then the month then the day. e.g., 2001/12/01 is
          ok, but 01/12/2001 is not, since 01/11/2002 would sort lower while it is later).  This is  because
          when using the rotate option, logrotate sorts all rotated filenames to find out which logfiles are
          older and should be removed.

Can anyone please tell me if "dateext" is correct? I want the log filename to be something like "access.log-2010-12-04".

Insert a dateformat directive to your configuration file, something like this:

 /usr/local/nginx/logs/*.log {
    daily
    dateext
    dateformat -%Y-%m-%d
    ...

One more thing: Can I do the log rotation every day on a specific time (e.g. 11 pm)?

By default, logrotate is running via cron at 4 A.M:

/etc/cron.daily/logrotate

#!/bin/sh

/usr/sbin/logrotate /etc/logrotate.conf
EXITVALUE=$?
if [ $EXITVALUE != 0 ]; then
    /usr/bin/logger -t logrotate "ALERT exited abnormally with [$EXITVALUE]"
fi
exit 0

You can move this file to somewhere and rename to logrotate.sh, then create a new file in /etc/cron.d/ as belows:

0 23 * * * root /path/to/logrotate.sh