Just like metaphors that are usually classified as either living or dead, I would think that this acronym could be classified as dead because the word "zip" seems to have taken on its own meaning that is not associated with the acronym. Also, this meaning of "zip" seems to have become accepted as part of the standard lexicon of English.
Interestingly, the OED lists the "zip" of "zip code" in lower case letters and does not mention anything about the need for capitalization.
After sending this comment, I continued to think about etymology and language change. Language is constantly changing and when a change in the definition of a word (or acronym, I would argue) becomes accepted as part of the standard lexicon that is when the original meaning is considered dead. The original, acronymical meaning of zip is "Zone Improvement Plan," as named by the U.S. Postal Service in 1963. I think it is noteworthy, however, that the Online Etymology Dictionary states the acronym was, "no doubt chosen with conscious echo of the verb zip meaning 'move rapidly'."
It is apparent to me that the "move rapidly" definition of "zip" has become accepted as part of the standard lexicon, therefore capitalization should be optional and could soon be obsolete as the acronymical meaning fades entirely.