Website intermittent load failure - something wrong with DNS?

Quick overview:

• Developed web app with Python and Django; developed and tested locally; adjusted settings to harden for deployment
• Deployed app to Heroku for simple hosting platform; tested and worked successfully
• Purchased hobby hosting on Heroku so deployed app would not sleep; I can still verify this to be true, the app loads instantly at myappname.herokuapp.com
• Purchased domain name on GoDaddy
• Used a free CloudFlare account to manage DNS
• Entire chain of operation works successfully sometimes, but sometimes I get a website coming soon page:

So when I go to bed last night, everything works. I can load the app from the purchased domain name on all my computers and mobile devices. I wake up this morning, and I'm once again getting the coming soon page. No matter how many times I refresh, and with cache disabled in Chrome so I know it's not my browser.

Everything is working perfectly on the Heroku side, since I can load the app there every single time. Once I told GoDaddy to use Cloudflare's nameservers I think there can't be an issue on GoDaddy's side. There has to be something with Cloudflare.

The DNS settings on Cloudflare are super simple:

• CNAME for my.url pointing to my.url.herokudns.com
• CNAME for www as an alias of my.url

The hardest part is that it just sometimes works and sometimes doesn't. I can't nail this down.