Objectivists, so I understand, say that altruism is a Bad Thing.

The analysis of Objectivism is further complicated by Rand's act essentialism. As I would characterize her view, it's the principle of the act, the intent of a policy involved, not the particular consequences that matter.

Just as life wasn't your living and breathing, but life "qua man", altruism for her would be an intended policy of sacrificing your values for the values of others, which is just what Comtean altruists suggest as the moral policy.

I care about other people.

Per Rand, your feelings are not the standard of morality. Acting because you feel like it is "whim worshiping subjectivism", per Rand. Me, I'm a whim worshiping subjectivist, so if you care about people and want to help them, great, knock yourself out. Where I part company with most altruists is on the belief in a duty to be altruistic. I don't condemn people who aren't altruistic, but instead have other values they wish to pursue, as long as they aren't infringing on what I consider to be the rights of others.

Does the Objectivist objection to "altruism", as you understand it, extend to all instances of the schema in the foregoing paragraph?

You have a prior problem with Rand here. You have not defined a moral code based on principles, but are making ad hoc evaluations of preference. You unprincipled, whim worshiping subjectivist, you.

That is, does it advise me never to let any benefit to others, however great, outweigh any loss to myself, however small?

You're analyzing in a different schema than she does. You're analyzing the particular concrete, while she analyzes the "essentials" of the act. The practical answer is no. Sometimes the correct moral code will seem to be a sacrifice of your interests to others in a particular situation. For example, she would be against stealing even when you're "sure" you will get away with it.

But if your intent is to sacrifice your values to the values of others, if that is the standard by which you judge the morality of the act, then you're acting on the basis of an evil moral code.