Its because its configured to make static pages in awstats...
What you can do is install awstats manually on the site (e.g. download from awstats web site, and upload to a dir), and config it to read the directory the txt files that AwStats creates...
We do this, and it works fine for our clients that really really want AWStats on their account. and they can view previous months etc...
EDIT: but make sure awstats is still configured in Plesk so it keeps creating the files etc.