In Once Upon a Time in America why did Deborah not let Noodles back in after he and Max were beaten up by Bugsy and his gang of thugs?
In the scene that shortly precedes the one you're referring to, Deborah and Noodles are alone in Deborah's father restaurant. It's Saturday and everyone else is gone to the synagogue to pray. Deborah is aware of Noodles presence outside the diner and when entering the premises she lets the door unlatched on purpose, hoping that Noodles will slip in, which he does.
In the back of the diner, amongst "the brooms and the empties" where she usually practices her dancing, she reads him the "Song of Songs" and reveals her true feelings for him, but warning him at the same time, while also mocking him, that they could never be together as long as Noodles remains a "two-bit punk" a street gangster ("what a shame"):
Deborah has understood that in order to be with Noodles she would be bound to give up her dreams of fame and glory, and she just won't do that, as she clearly explains to Noodles few years later when they are dining in the exclusive restaurant by the sea (the following quote is circa at 2:15 in the subsequent clip) :
Deborah: Noodles... you're the only person that I have ever...
Noodles: Ever what?
Noodles:: Go ahead, ever what?
Deborah: ...that I ever cared about. But you'd lock me up and throw away the key, wouldn't you?
Noodles: Yeah. Yeah, I guess so.
Deborah: Yeah... and the thing is, I probably wouldn't even mind.
Deborah: So... I got to get to where I'm going.
Noodles: And where's that?
Deborah: To the top.
Noodles: Now you sound just like Maxie. You's both alike, that's why you hate each other.
Deborah, just as Max does, wants to go as far as possible from the place where she grew up, whereas Noodles' attitude is completely the opposite:
"I like the stink of the streets. It makes me feel good. And I like the smell of it, it opens up my lungs. And it gives me a hard-on."
And Deborah also knows that Noodles puts friendship and loyalty above anything else, above his own good and that he will always respond to Max's call ("Go on, Noodles, your mother's calling you", she mocks him).
When the teenage Deborah refuses to open the door to tend to Noodles wounds that has just been beaten up by Bugsy and his gang, she does it because she wants to shut him out (literally and metaphorically) and because she doesn't want to be dragged down by him, as she knows she would be if she lets him in.