I have seen many WordPress blogs taking this approach. They use to close comments after 30 days or 2 months of writing the blog post. So if you have some current affairs blog or a blog that updates your on offers & price of products, you can think of trying it. But I am not a big supporter of this method. Even with those blogs you may want to comment something so that later users get the correct info for that time. Only solid reason that I find is for dofollow blogs. If you have a dofollow blog, other webmasters might try to take advantage & there is every possibility that they would make a meaningless comment on an old blog post that has nothing to do in current context.
So now I will just tell you how to do it because the choice is up to you
So to close comments on WordPress blogs after some specific days just go to Settings> Discussion from your WordPress dashboard. Search for the line “Automatically close comments on articles older than” & then you can find the option to specify the number of days after publishing the blog post. Don’t forget to check the checkbox & save it. You are done. Comment option for all of your WordPress blog posts will now get closed after that specified days.