This is my stats update line plus my "fix" line.
Make sure to edit "user" and "domain.com" to make your paths correct. In my example, my awstats program is in the /home/user/awstats directory, and my statistics output is in /home/user/domain.com/statistics. If yours is different, be sure to change this.
Mine is set to run the stats update at Midnight, and move the files at 12:02am.
Also, I've added a bit at the end that stops it from emailing me every time it runs. If you would rather it email you, remove the "> /dev/null 2>&1"
The below code should be on TWO lines only. Otherwise will not work.
00 00 * * * perl /home/user/awstats/tools/awstats_buildstaticpages.pl -config=domain.com -update -awstatsprog=/home/user/awstats/cgi-bin/awstats.pl -dir= /home/user/domain.com/statistics/ > /dev/null 2>&1
02 00 * * * mv /home/user/awstats.domain.com* /home/user/domain.com/statistics