Ethicists seem to have started talking extensively about moral status at some point in the mid-eighties; although there were precursors in the seventies, the widespread framing of ethical problems in terms of moral status was not common, if it existed at all, prior to then -- people would use the term loosely and colloquially before that time, but not as if it were a recognized technical term. And one of the things that one notices if you review the things that have been said about it is that, if we take it as if it were a technical term, or a quasi-technical term, it is incoherent; not only do different ethicists not mean the same thing by it (it is common whenever discussing it simply to stipulate what one means by it), even key accounts of moral status by notable ethicists of moral status are not coherent with themselves. At times it is so expansive that 'having moral status' means merely 'being able to be considered as part of moral reasoning'; at other times it is so restrictive that it deals with only a tiny slice of moral life. And not only is it incoherent, it is otiose: it contributes nothing to the discussion that could not be handled simply by being more specific and less equivocal, both of which are good qualities to have in discussion of ethics, anyway.
Nothing has moral status in a technical sense because moral status, as found in technical discussions, is a fictional, incoherent, and useless concept. I keep telling this to people and they keep looking at me like I'm crazy. But I am far from the only person to say something like this, even if most people tend to soften the claim a bit. Benjamin Sachs had a really good paper on this in Pacific Philosophical Quarterly last year; I think it's one of the single best meta- papers on ethical inquiry that's been published recently. It is available online:
The Status of Moral Status (PDF)
It really should be read by anyone who talks about ethical issues, and no one should be allowed to use the phrase moral status as a key part of their discussion without expressly addressing the issues raised in Sachs's paper. It is also, I should say, eminently readable. You don't have to agree with every part of it to recognize it as a beautiful paper.