reasons for your adverts and posts 'disappearing' will either be you haven't selected 'keep me logged in' on the log in page, your cookies settings are having a mdlife crisis or you have your security or computer sharing settings set wrong for your usage.
All good suggestions
However, his posts are all publicly visible; you don't need to be logged in or even have an account on here to see them. The World and his brother can see them. In this case cookies are irrelevant, as previously stated, you don't need to be logged in to view this section of the Forum, cookies are only used to keep you logged in - if you want to be. Security settings on the computer; if he can get to this site then the settings are good, he will be able to see everything.