Need implies no rational argument exists by witch you can have a short story without a definitive ending. Lady and The Tiger exists, therefor short stories do not need a definitive ending. QED
Perhaps at a greater philosophical level no story needs to have a definitive end. And there's a whole thought process that goes into saying stories can't end, can't begin as they're always being told. The players and cast change overtime, but time continues in both directions without exception.
Stories are usually a little more concise than all that. So, what you're looking for, really, is whether the primary point of conflict being dealt with is resolved. Even in lady and the tiger the primary point of conflict is resolved, we just don't know how.
You're not asking if something can have an ambiguous ending, so much as whether you can tell a smaller part of a story. Let's flip the question on its head; because you can obviously write whatever you want and rephrase it:
Will readers read a collection of short tales that are part of a larger scheme and don't resolve a grand conflict?
Yes, and they do all of the time. The trick is to give people a bite that is both interesting and satisfactory. Successful short stories tend to arrive at a point where its clear things have changed, but they often do not resolve everything. They can't, there's not enough space. As long as its clear that the current events have caused a change and that change is very interesting the text can serve as a short story. People will still want to have enough information to feel like there's progression of a sort, but unlike a novel you can never deliver everything.
I would caution you to not have "cliff-hangers", as in sudden reveals with a "find out next time". If you're doing that, you're writing serial fiction, which means you are committed to writing more. Which is fine, but that's not telling a short story. A short story should be like a course in a meal. It should feel complete unto itself, but part of something larger all the same. It may leave the diner hungry for more or cleanse their palet; but it should serve a purpose and do it satisfactorily, automatically even if it a part of a larger tale that is richer when viewed as a whole.