Isn't the risk that your negative results harbour a poor experimental methodology, a deficiency in technique or what have you.
That's a pretty big reason not to publish a negative result, especially if the original result has social credence (big name, popular publication, wide acceptance).
Are negative results more likely to have methodological or experimental error than positive results? I've never heard that claim.
I would actually expect the opposite, as finding evidence to support a new claim should be more difficult than not finding evidence.
My understanding is that a negative result has the following format: "we did such and such experiment and did not find a significant statistical relationship between thing 1 and thing 2, after controlling for a bunch of other things".
It's worth noting that this by no means proves that there isn't a relationship, it just means that study wasn't able to find evidence of one. It could be a piece of the puzzle for a potential strong case against such a relationship, or that further research is needed to untangle any confounding factors. Which is why I think all methodologically sounds results should be published, no matter how unflashy or boring.
That's a pretty big reason not to publish a negative result, especially if the original result has social credence (big name, popular publication, wide acceptance).