The new posts is not limited to 1 day. However, most days there are more than 500 active threads which is the upper limit returned by search so may be why you arent seeing older days.

You can create your own search for forums you frequent and showing a greater number of days by using the standard "Search" function. Can even save your search settings to make it quicker to reuse.

I agree with you that New Posts function is very handy ^