Achilles' heel or achilles heel? - Is it proper to lowercase the usage

I was reading an article that uses the phrase "Achilles' heel" to refer to Facebook's acquisition of Instagram, but it was written thus:

achilles heel

My main question is - was this a bad mistake or is making this kind of description in this way a common thing? If so, could you provide examples where others have taken common phrases and lowercased them.

A little more context in case it helps:

Because Facebook is essentially about photos, and Instagram had found and attacked Facebook’s achilles heel — mobile photo sharing.

Solution 1:

Achilles is a proper noun. However, this ngram does seem to show some extremely slight/rare incidence of the lowercase form.

That doesn’t make it “right” or generally accepted.

Solution 2:

Much like a genericised trademark, many terms that were originally derived from proper names have evolved over time into ordinary words:

• quixotic—Don Quixote

• boolean—George Boole

• abelian—Niels Henrik Abel

• chauvinistic—Nicolas Chauvin

• sadistic—Donatien Alphonse François, Marquis de Sade

• erotic—Eros

Therefore I would say it’s acceptable to use the lowercase form, achilles heel.