"... What happens if Disqus goes out of business? Do all of your comments evaporate? ..."

A quick look at the website would reveal, "No" ~ http://disqus.com/help/#faq-6

  I use Disqus because it gives me 
  "the freedom to leave" at anytime

Understand that data "Lock-in" is the new "Lock-out". If Disqus does collapse, I still have my data because I have access to it now. To understand why this is important read about "The zen of free" ~ http://asay.blogspot.com/2006/06/simon-phipps-on-zen-of-free... by Simon Phipps.