OK, I had this exact same problem (and still do). I think it's a glitch in the fish AI that severely decreases the chance of them biting. I did however manage to catch a Reekfish with a worm attached, but it took about half an hour. It's super frustrating but I think if you keep at it, you'll get the fish and not have to restart the game and hope the glitch gets averted (restarting that far in would suck).