Facebook Developer Invitation for a Facebook App not received
UPDATE FEB 2020
This issue is still relevant and happens from time to time. If notification is missing, then invited person should navigate to https://developers.facebook.com/requests/ and accept invite there.
Not sure why this got downvoted, I was having the exact same problem the other day. The problem may be that, like me, you're expecting to see a message from Facebook (via notifications) about this. That's not how it works. You will get a developer request, which will show up on your requests panel--this thing, which appears in the right-hand column:
At the bottom it should say "1 developer request". Click through to that and approve the app, and you should be good to go.
I was having issues with the Facebook UI for accepting Developer requests, trying to view them just recursively took me to https://developers.facebook.com/apps?view=app_requests.
Jumping here allowed me to accept the request. https://www.facebook.com/reqs.php
Go to https://developers.facebook.com/requests/ to check your application requests.