system
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Wilf -
I am currently using a computer with W98SE and do not have a problem with it shutting down when I tell it to do so. Of course, I am also using avast!4 Home. So, avast is not the problem. 
Perhaps this problem showed up after installing avast because your computer was already close to having this problem? ???
Years ago, I did have a shutdown problem with W98SE but installing the MS patch cured the problem ever since. ;D
While you are at Windows Update looking for this patch, be sure to get all other patches/updates available for your computer. 