Hi,
You can do that by editing the domain's awstats configuration file. The configuration file located at the following location /home/USER/tmp/awstats/awstats.DOMAIN.com.conf. You can edit the following variable to enable the awstats update for the domain.
Look for "AllowToUpdateStatsFromBrowser=0" and change it to:
"AllowToUpdateStatsFromBrowser=1"
That is it. try a restart for your cPanel service. Everything will be fine after that.
Thanks