A lot of people believe that "conventional science" often seeks to cover up or ignore anything which challenges accepted beliefs.
In some cases this is probably true but as a generalisation I believe it is completely wrong. I think it is based largely on a misunderstanding of what scientists are like as people. When you think of scientists as individuals and put yourself in their position, it becomes hard to imagine them all being involved in any sort of large-scale conspiracy.
Scientists love to uncover new information and they love being the first to do something. Making a discovery or proving a theory that rocks the scientific world is every scientist's dream.
If some radical new or alternative theory could be proven to be true, there are very few scientists who would back away from the chance to be associated with it. For example, if a study was able to demonstrate ESP to the satisfaction of a good scientist, that scientist would certainly want to publish their work. This would be an astounding breakthrough that would assure them a place in history.
In turn, once a valid study has been produced, other scientists would be rushing to replicate the results. Getting on the bandwagon early is the next best thing to making the discovery yourself.
Note: This is an important point when considering studies which do support paranormal phenomena — if they are valid they should be attracting widespread support. The only reasons for other scientists not to offer support is that they can see faults in it, or they have tried and failed to validate the results.
I personally find it hard to believe that evidence for anything paranormal is being routinely covered up. It's too big and the motivation to go public is too strong. There's no way it could have been kept under wraps.