Downtimes and suffering rarely respond quickly to your site and your old posts more static, as this also removes some of visitor interaction, and then I would not recommend to close the old post comments.
Q: Why can not help you here on the site of the old post comments stop feeling sluggish lately, and if you are being told: You do not notice it, even if your blog is sometimes dozens, hundreds and even thousands of comments every day gets. How come you do not notice them? It is because of the spam comments and Akismet (or whatever you use anti-spam plugin) for the catching.
Identifying and filtering out all those spam comments, it is understood that the processing requires some processing power, and the fact that your server runs a little faster by turning off the old post that is why.
Your comment if you just inside your dashboard> settings will be discussed. I have chosen to turn off the 7-day old post, but I had no problem of spam, because it is that. As in your case is not severe, then 30 or even 60 days is very fine.
Finally, sometimes the designers had not planned this as your theme, do not forget to check how they will be closed with the comment, and it is a