The matter is that the hypothesis is not disproved. From a statistical point of view, H_0 not rejected just means that we can not exclude that the difference (or the correlation) between two or more variables would be attributed to the chance (that is, the sample variance). The outcome is, of course, informative. If we organize many well designed experiments, and none of them is able to confirm the hypothesis, we can reasonably conclude that it can't be proved. The null hypothesis, however, is not as strong (in disproving a theory) as the alternative hypothesis is in proving it.