Why is my app post deleted?
My guess is that an automated process did this. You can still view the post, just copy the URL from the 'Manage your applications' page. If it has a banner 'deleted by Community ♦' that's the case.
Should I just create a new post to get API access?
That's fine (it's not that we're flooded with new posts every day). Something that helps to avoid this in the future is to properly document your app, instead of only using a placeholder. It's more likely to receive an upvote (at least from me) and questions with a positive score are never deleted automatically. (If you already did this, perhaps I missed the post.)