I can see how the idea of falsifiability (rather than some form of verificationism) could support a demarcation between science and pseudoscience. Here is the Wikipedia definition of falsifiability:
A statement, hypothesis, or theory has falsifiability (or is falsifiable) if it is contradicted by a basic statement, which, in an eventual successful or failed falsification, must respectively correspond to a true or hypothetical observation.
Does that "basic statement" have to be a reproducible basic statement? I don't think it does, but I don't know what Popper says about this.
For example, suppose we observe a dust cloud approaching Sagittarius A* where a black hole is supposed to exist. We predict, using our falsifiable gravitation theory, that the dust cloud will be absorbed in some way by the black hole at a certain time. We get only one chance to observe this. It is not a reproducible event. But I think that prediction of the dust cloud's absorption would still be considered a "basic statement" that could contradict the theory.
I am looking for quotes from Popper on this topic since I would like to read more about what he had to say and perhaps quote him later.