Image: Cold Souls (film)
For the so-called skeptics amongst us to believe in something they require scientists and scientific establishments with strong reputations to conduct research that supports the contention. In the case of PSI research there is a great barrier to established scientists and institutions working in the field- the lack of prestige such research generates. There is also no money in it. Only a scientist with no interest in building a career and participating in the current research funding model is likely to work in the PSI field. And the results of this research are likely to end up in a dusty old journal that nobody reads. So it's a dead end for an ambitious scientist and it's unattractive for even an unambitious scientist who just wants a solid unheralded career in science with a decent income.
Those who are experts in the PSI field say that PSI has already proven itself scientifically in a multitude of well-constructed trials. However, this is irrelevant to many people, including skeptics. They only trust scientific results when, either, they support their own cherished beliefs or when they are undertaken by scientists they are familiar with and hold in high regard. As established scientists avoid PSI like the plague (to avoid having their reputations trashed) this will not happen anytime soon. Otherwise, skeptics easily dismiss the undesired results generated by unknown scientists as being biased or the result of poorly constructed trials.
For these reasons it is unlikely that skeptics will be convinced of the reality of PSI anytime soon.