You mention that your site has an unusually high number of Google and Facebook likes...this might very well have something to do with the high ranking as a more visible site tends to perpetuate its ranking initially in such a fashion. How long have you owned the domain and what type of site was it before?
I would be interested to see if the site continues to enjoy its high ranking for more than a month or so. Don't forget the "new site bump" that you will get with Google for the first few months after a site is visible. I have seen a site rank on the first page for a few months, then disappear for a few, then reappear.
Like sarettah said, I need more specific info to be sure, but I don't think your site is "slipping through" the engines.
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