cling to the/(one's) belief that (something is the case)

To remain devoted to or entrenched in one's conviction or opinion that something is true, especially in a desperate or obtuse manner. A shocking amount of people still cling to the belief that the Earth is flat. That corporate bigwig is still clinging to his belief that he is immune from prosecution. I know this has been an exhausting, arduous process, but we must cling to the belief that things will work out in our favor!