It's an interesting question. I think this is very context dependant, what are the items that are being listed and more importantly how is the addition of more items handled? If you're showing a list that is being continuously updated you want the user to be able to update that list using any criteria for filtering that they may have added. In this case you definitely want the filtering settings to be present after a page reload. In this situation the user most probably wants access to the latest addition of items of the list that they have in front of them.
However I would argue that if you display something that is static, a list that will never be updated (like a table of content for a book) it would in my mind be OK to remove filtering settings on reload. I feel that in that situation the user is probably looking for a way to go back to the initial state of the content, looking at the whole rather than the filtered down part that they're currently observing.