It is precisely this repeatability by anybody, at any time, as many times as desired, and under perfect control, that physicists prize in their experiments and consider to be the hallmark of "scientific truth." Conversely, if something does not meet these standards, then we refuse to think about it or discuss it, at least not as physics per se. We leave these questions to other disciplines, and we uses the words "hard" vs. "soft" to describe how well a discipline conforms to the scientific ideals of repeatability and control, with physics on the "hard" end of the spectrum. ("Hard" vs. "soft" has nothing to do with how difficult the fields actually are.) For instance, astronomy has the problem that the stars are not under our control and we can not make them repeat their behavior; however if ten astronomers look at the same star at ten different times they will almost certainly see the same thing, which is a sort of repeatability. There is also a statistical repeatability in astronomy: picking a thousand stars at random, you always find roughly the same number of red giants, white dwarfs, Sun-type stars, etc. So astronomy is not as "hard" a science as physics; we can also say that it is a "softer" science than physics, which means the same thing. Going softer, one can speak of sociology, the study of large groups of people. From a scientific point of view this is worse: not only are world's people out of the scientist's control, but their actions, demographics, characteristics, opinions, etc. change from year to year and even day to day. The only sort of repeatability a sociologist can hope for is by running two or more similar measurements/surveys/censuses at roughly the same time. Softer yet would be psychology/psychiatry, where one finds a few things which recur, like the addict's acquired physical dependence on drugs, or oedipal complexes, but these recurring elements occur in a multitude of variations unique to each subject and constitute only a small portion of the overall field of study.
Then there are many fields which are not properly science at all. Most of these have their roots decidedly outside of philosophy, and emphasize the practical or functional side of things: law, engineering, the arts, history, accounting, etc. These are often called professions. However there are at least three disciplines which are rooted in philosophy and therefore are not in the same class as the practical professions, but are not science either. One is philosophy itself, which has parted ways from natural philosophy by steering away from experiment. Another discipline is theology, which is rooted in philosophy and does emphasize very careful attention and thought about the world around us, but focuses on unrepeatable aspects of that world, namely persons and what they do, say, and write. If natural philosophy is the philosophy of repeatable things, theology is the philosophy of unrepeatable things, of persons. A third philosophical but non-scientific discipline is mathematics, which concerns certain results which can be reproduced on demand, but which are not part of the physical observable world.
Of course a lot of times there is a secret to repeating something; you have to figure out all the necessary preconditions. Finding out how to make something repeat can be part of hard science. For instance a few years ago someone reported observing a fusion reaction occurring fairly slowly, in smallish laboratory. Previously fusion had been observed only in the sun, thermonuclear bombs, and large experiments involving very large amounts of energy and heat, so the new observation was very exciting. Over the next years many many physicists spent a lot of time trying to make fusion happen in their own labs, using similar equipment. Some report that they found evidence for cold fusion, though their evidence was pretty subtle, the sort that requires very special measurement equipment, quite far from nuclear explosions. However many physicists failed entirely to reproduce cold fusion, and this happened so often that the scientific community as a whole remains sceptical of those who continue to report cold fusion in their labs. So here we see that the question - is cold fusion repeatable on demand? - is a valid question for physics. However as it became clear that many skilled researchers are unable to reproduce the original result, cold fusion moved out of the domain of hard science, and the physics community stopped thinking about it. If someday in the future someone did figure out a recipe for reproducing cold fusion on demand, then suddenly it would become again a physics question.