I found this article on cloudflare.com that may help:
Also, what I'd suggest is to temporarily take your website away from a 3rd party caching service (such as cloudflare) and try running it for a week like that and observe your server logs to see if anything unusual is going on. Also, test it a few times in webpagetest.org to see if the loading times are acceptable.
Also, get a tool that scans every link on your site to make sure they are all valid. I use Xenu Link sleuth (found at http://home.snafu.de/tilman/xenulink.html#Download).
Once things are acceptable, then try cloudflare again and if you still get HTTP error 520, then there is something wrong with either their service and/or with your account on their service in which case you should contact them directly about the issue.