I remember an issue with PageHitCounter a long time ago where each visit resulted in exactly this behaviour.
So in case you use that module, update that as well but check for update instructions as there have been some in the past.
Another possible solution is your custom code in either the template, a module, or a hook.
Hard to tell without knowing more about the template, possible hooks, and similar things.
Do you do anyting with the API, like updating or creating pages, entries or whatever?