We are right to hold discoveries of science and the scientific method in high regard. But that approval is distinct from respecting scientists as a class. The problem of non-reproducibility is no fault in the scientific method but instead indication of the rotten state of modern academia.
Earlier in my career I worked at universities writing software used for psychology and neuroscience experiments. On the basis of that experience I can offer an explanation for why about 1/2 of experiments are not reproducible: A lot of psychology faculty are terrible liars. While some demonstrate perfect integrity, others, probably the ones generating all those irreproducible results, lied whenever it suited their purposes. Still others were habitual liars who lied not to achieve some specific outcome but out of habit or compulsion. The center director of one research group confided to me, after a dispute with the faculty, that he had not been able to control his compulsion to lie. And when I claim that faculty "lie", I do not mean what could, by any stretch, be characterized as errors, oversights, or honest differences of opinion. I mean abusive, sociopathic, evident and deliberate lying. Like being told that the inconvenient evidence which you have in hand, "does not exist."
The lying is enforced by implicit threat. One time I responded to an email message, correcting an error, and then immediately after that a prominent member of the faculty, somewhat creepily, follows me into the restroom, stands too close to me while I am using the urinal, and explains to me in a threatening tone the error of my reasoning, which according to him, was that, "it would not do that because it would not do that." The dean imposed a disciplinary penalty on me for objecting to that. Though that was unusual, typically challenging lies elicited, a yelling, screaming fit from a faculty member. So it's not just lying, but lying backed up by threatening, thuggish, behavior of the faculty and university administration. This was a highly-regarded department with generous NIH funding, which makes me think that lying in that field is kind of a mainstream thing.
The root cause here has little to do with science, per se, and has more to do with the rotten management of colleges and universities. Regardless of what the employee handbook states, there are few de facto restrictions on faculty conduct and university administrations act to cover up problems by disciplining and threatening the whistle-blowers. Jerry Sandusky was not a scientist, he was a football coach, but if you look at the way Penn State concealed child molestation and protected him, that is typical of the way universities respond to faculty misconduct as welll, and explains why academic dishonesty is tolerated. One full-time faculty member in the department in which I worked had not set foot in the department in over five years nor ever appeared in any of the classes which she "taught." According to the department chairman, every time she was contacted to encourage her retirement was, whe was, "drunk off her ass in the middle of the day." It was tolerated and covered up.
I am not claiming that all scientists, fields, or academic departments are full of liars. I have never worked closely with physicists, computer scientists or mathematicians on a daily basis, but none whom I know personally have behaved like that.
To sum it all up, psychology has a problem with poor reproducibility of published results, many of the psychology faculty I knew were terrible liars; there might be a causal connection between the two.