Etymology is not a determiner of whether something gets capitalized or not. Many proper nouns are derived from non-proper nouns (e.g. Apple, Smith, United Kingdom, World Wide Web), and vice versa (e.g. atlas, echo, narcissist, siren, sodomy). It is usage and usage alone that determines whether something gets capitalized or not. In fact quite a few proper nouns become genericized against the owner's will because of usage. Examples of nouns created that way include aspirin, bandaid, coke, escalator, kleenex, thermos, zipper; examples of verbs include google, photoshop, facebook, and skype.
Of course when you coin an all-new verb — say, to AltaVista, to iPod, to McDonald's, to NATO —, capitalization is instrumental in helping readers understand what on Earth you're talking about at all. But once a verb has entered everybody's everyday lexicon you'll be hard pressed to justify capitalizing it, especially if it's taken on a generic meaning, and especially seeing how English, in general, simply does not capitalize verbs except at the beginning of a sentence. "I googled for photoshopped cats and had to lol" becomes the norm, not an exception.
Edit: I tried to have a quick look at actual usage, but both COCA (three cites for "skype*.[v*]", all SPOKEN) and BNC (no hits at all) were not exactly helpful.