In a comment posted years ago to the question Why is "biblical" the only proper adjective to not use upper case? I listed some other exceptions to the general rule that the first letter of an adjective derived from a proper name is normally capitalized. Only the letters q, w, x, and y did not yield an example (for some reason, I failed to notice quixotic):
arabesque, byzantine, caesarean, draconian, epicurean, faradic, galvanic, herculean, italic, jesuitical, kabbalistic, lilliputian, mercurial, nazi, oedipal, pyrrhic, rubenesque, spartan, terpsichorean, utopian, voltaic, and zephyrous
Why do these exceptions occur? The not-very-satisfactory answer seems to be that common usage determines whether an adjective based on a proper name is initial-capped or lowercased. Dictionaries provide their spelling preferences based on what amount to the found objects of preponderant real-world usage in each case; and thenceforth, real-world usage (to the extent that it is influenced by people who look things up in dictionaries) tends to reflect the dictionary treatment. The very circularity of the process makes it extremely difficult to determine where and when the critical decision regarding initial cap versus all lowercase got made.
I don't see how else to explain why Oedipal is usually initial-capped when it refers to the mythical character Oedipus (as in "Oedipal resistance to fate") but usually lowercased when it refers to Freud's Oedipus complex (as in "oedipal feelings"), although the complex is explicitly named after Oedipus.
Bryan Garner, Garner's Modern American Usage, second edition (2003) concludes that trying to explain exceptions to the normal rules about what gets capitalized and what doesn't is a fool's game:
There is simply no way to reason out why Stone Age is capitalized but space age is usually not, why October is capitalized but autumn is not, why in scientific names the genus is capitalized but the species is not—even when the species name is derived from a proper name {Rhinolophus philippinensis}.
Ultimately, capitalization conventions rest on strong general tendencies tempered by exceptions that are neither consistent nor explicable.