IS there ever a time, where forums should delete old posts, like if there
haven't been any views in awhile, or should posts be like a permanent
archive?
Unless you are really big, leave them there (unless they are bad posts). If your forum has 1,000,000 posts, deleting a couple hundred won't matter, but if your forum has 1,000 deleting a few hundred would be bad.
I think the only posts that should be deleted are spam posts. Other then that you should only delete posts if your host has a limit on the max size of your DB in which case i would consider moving hosts before you reach that anyway.