They seem to be a bit buggy, but what seems to fix it for most people is to turn them off and on again.
Go to your account settings and move your “Receive WaniKani Related Emails” from Yes to No, and then back to Yes. (Note that there’s a different setting in the “App” section of the settings that is about your review and lesson counts. That’s not the one you need to toggle).
After turning them on you should receive the one you missed for level 6.
There’s also a thread with all level up email contents, in case you never manage to get yours and are curious about what it says.