The phrase "persistent rumors" means that there are ongoing and continuous rumors or stories circulating, which are repeatedly heard or talked about. Full definition
Let's take a look at the most persistent rumors so far. (mypotatogames.com)
Now the question is whether persistent rumors that the experiment has detected the long - sought waves are accurate. (sciencenews.org)
Some even claim that the creation of the card was inspired by persistent rumors and urban legends of an ultra secret black credit card that the super wealthy could use to purchase anything. (rewardexpert.com)