When I post a short simple answer to a posted question and someone downvotes it, they should be able to explain their objections if I so request. During the months I've been here, I don't recall that any such requests from me have been ignored until it happened twice within the past week. Could there at least be some officially promulgated norm about politeness and about respect for the fact that we are here for a common purpose, that says something about this?
No, it is not abusive to downvote for no stated reason.
There is a discussion on meta.SO about this. While all the answers and comments are interesting, the answer given by Jeff Atwood, one of the two creators of the StackExchange network, says that people do not need to explain their downvotes (or at least, not enough so that they face any repercussions from not doing so), but a reminder that one can explain one's downvote with a comment is implemented for users with <2000 rep.
Also, my own opinion is that it is only abusive to serially downvote a single person's posts out of spite, which in any case would automatically create flags, moderators would take care of things, etc. Requiring an explanation via a comment means loss of anonymity of downvotes, which I consider to be extremely important (as did many of the commenters in the discussion linked to above), and perhaps the downvoter has to attend to something else at the moment, or thinks the problem with a post is so blatantly obvious it doesn't need an explanation. If an answer is absolutely abysmal, it's a waste of everyone's time to have to post a comment - it is in the best interests of the site to make sorting the site's content by value as efficient as possible. Requiring an explanation to accompany every downvote would be such a large drain on everyone's time that vastly fewer people would bother to downvote, which would thereby harm the site.
Downvoters do not necessarily see the requests to explain their votes.
I agree with the sentiment that downvoters should ideally explain their votes. My posts haven't been voted down too often, but whenever I see anonymous downvotes, I usually request an explanation irrespective of the poster. That said, I agree with Mariano's comment that this shouldn't be an obligation on the voters.
I am also a bit puzzled about the exact suggestion made by the OP.
Could there at least be some officially promulgated norm about politeness and about respect for the fact that we are here for a common purpose, that says something about this?
What would be the benefits of such a policy (even assuming we all agreed on one)? Whether
the downvoter forgot to explain the vote and also missed the request for the explanation, or
the vote is just a hit-and-run case,
I don't think we'll be any more successful in enforcing this official policy, given that the chief issue here is the anonymity of the vote. If all that the downvote victim could do is to post a comment and hope for a response, isn't that what we're doing already?