Is Sheldon ever shown to succeed at research?

This is one of those ways in which the research on the show utterly fails to reflect how real science is done. Of the examples you listed which were presented as failures:

• His antarctic research is based on faked measurements

This is serious scientific fraud, assuming it made it to publication, and in reality would cost the entire group their careers. (But then we wouldn't have a show.)

• In the paper which Leonard is presenting (and gets distracted), it is presented as Leonard really doing most/all of the work

This sort of thing happens all the time in science. Some authors do most of the "grunt work" of the project, and others get their name on it for lower-effort contributions like offering the initial idea. It's also very common for authors of a joint paper to disagree about who contributed most to the project, and so depending on who you hear talking about the work, you might get a different impression as to who did the most. (It's not common to fight over it.)

In any case, I see no reason to consider this a failure.

• The paper he gives to Stephen Hawking contains a "booboo"

Sheldon is a perfectionist, in this scene even more than usual because he is having a paper reviewed by his idol, Stephen Hawking. I bet the booboo he gets anxious about is something like a sign error or a factor of 2 buried in a complex formula in the middle of an argument. Little mistakes like these occur by the thousands in published physics papers, and real physicists learn that, while it's certainly important to try to catch them, these mistakes are not worth caring about after the fact as long as they don't affect the paper's conclusions. So again, not something I would consider a failure.

• He retracts his discovery of the super-heavy element

If I remember correctly, the element was discovered anyway thanks to his research. It was just the particular way in which Sheldon showed its existence that was flawed and needed to be retracted. That's the best kind of success: he was responsible for the discovery of a new element (doesn't matter that it was by accident) and there's a great story about how it happened, to boot.

---

If you want an example of a success, perhaps you could take the time Sheldon figured out that electrons propagate through graphene as a wave while he was working at The Cheesecake Factory. The physics involved was actually very simple, but Sheldon certainly acted as though he'd made a major breakthrough.

Speaking more generally, Sheldon's status at the university in combination with his age strongly suggests that he has had a phenomenally successful research career, which we simply don't see much of in the show. You don't get to be a tenure-track professor at Caltech in your 20s unless you are literally at the top of your field, like among the top 5 theoretical physicists in the world. I think we simply don't see the successes because failure is funny; success is generally not.