Moving to typekit.
I replied to your email to Typekit Support (firstname.lastname@example.org) to get some more information on the problem. Once we figure out why Typekit isn't working for you, I'll update this forum thread with the solution!
An update for the forum thread:
We weren't able to reproduce the problem on the website, but one of our engineers took a look and believes it's related to the prefixfree.js library.
Prefixfree.js has caused problems with Typekit font loading before, and the issue is intermittent, as it depends on the relative timing of when prefixfree runs vs when the Typekit fonts are loaded into the browser.
This library is included with some website templates or themes by default, and you may not be using it. If you don't know that you are, the first thing to try is removing (or commenting out) this line from the site.
If you think you're seeing this same problem on your website and removing prefixfree (even temporarily) doesn't solve it, drop us a line at email@example.com and we'll take a look!