Sounds like you are going to have to tear part of the wall out and take a look, unless the tub has a removable skirt. You might be able to remove the front trim of the overflow and take a look in there with a flashlight and maybe a small inspection mirror - you might find that it has cancer or if plastic, cracked. If you are really lucky, you might just need to tighten something up, but I doubt you'd be able to get to it without tearing out a protion of the wall. Maybe someone else will have some otherideas.
How old is this, and did it ever work right?