jonkern

Keep it Fresh will stop WordPress from showing posts older than a set number of days or a specific date. It is configurable via the WordPress administration area. Keep it Fresh doesn’t remove old posts, nor does it muck with their <code>post_status</code>; rather, Keep it Fresh uses the <code>posts_where</code> WordPress filter to filter out posts older than the given date or amount of days whenever WordPress requests posts outside of the admin area.

Keep it Fresh

Keep it Fresh will stop WordPress from showing posts older than a set number of days or a specific date.

nestwiderhaken

Shows only posts, that are newer, than the day the current logged in user was created. 
This plugin is only useful if you have an other plugin installed forcing any visitor to login first. 
In that combination you get a blog in which the posts of older users are invisible for new users. 
None of the old users must therefor worry about statements made in older posts becomming available to users he don’t want. 
In the moment a user publishes a post, the amount of authorized readers for this post stays the same.

Only New Posts

Works fine.

Shows only posts, that are newer than the day the current logged in user was created.

Keep it Fresh vs Only New Posts