This is a question that we ask ourselves, too. When we're told to write a research paper or essay on a relatively small sample of writing, like a short story, it can be somewhat scary. How can we write at length about something that isn't even that long?
Of course, some short stories are long, like James Joyce's "The Dead." Other short stories, like Langston Hughes's "Pushcart Man," are only a couple of pages.
Fortunately, the length of the short story doesn't prevent us from speaking about it at length.
Maybe think of research papers (and essays, reading responses, and what have you) as ways to demonstrate to your teacher that you have thought about what you read and are able to articulate these thoughts.
F. Scott Fitzgerald (who wrote his fair share of short stories) said,
The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.
In your research paper about your short story, show off your first rate mind and tell about all the colliding ideas in your head.
If I were you, I would start with a thesis. Say that I was writing a research paper on Hughes's "Pushcart Man." What I like about the short story is how none of the characters have regular names. There's no Karen or Bob or George, but there is a "fellow in a plaid shirt" and "a guy leaning on a mailbox."
So my thesis would have to do with names and how there's all sorts of ways to identify a person besides using their name. I could discuss the creativity of using a non-name. But I'd also tell how not using someone's name could be seen as harmful and reinforce negative stereotypes. I might even bring in an article or two about names and the various meanings of having a name and having other people acknowledging that name.
That's a lot for me, and Hughes’s short story isn't even that long. But that's something you could apply to your own short story. Focus on a theme or character or scene that caught your attention and then dive into all the ways it captivated you.