SS stores the comment name, email and url in a cookie. though it shouldn't store the comment text. If it stores comment text you may want to check if you have partial caching or static caching enabled. In those cases you'll need to disable caching for the comments area.

All SilverStripe sites will have a cache folder. The cache will contain at least a manifest of all the classes used but in the event of using static caching (i.e if there are .html files in that cache folder) then you will need to disable the static cache for those pages. Or if you see <% cached %> in your template file then you can wrap the $PageComments variable with an <% uncached %>$PageComments<% end_uncached %>.