I have come across this situation before on just a couple of occasions. In those cases I did not believe it impossible that the person could learn to fly. I did think that they would be throwing a lot of time effort and money at it. At the end of the day it is there decision if they want to continue and who am I to tell them what they can or can't do? Just as long as they are making an informed choice, and I have made sure that they are aware of how I feel they are progressing.
In one of these cases we subsequently found the student was regularly working upwards of 80 hours per week and sleeping a whole lot less than he should have. It was amazing he could fly as well as he was! In his case it was subsequently proven that with adequate rest he flew very nicely indeed.
In other cases I have recieved students at the school who had been told by previous organisations that they would never learn to fly, and have delighted in getting them up to solo and beyond. Sometimes instructor and student just do not gel.
Before you decide it is a hopeless case, consider that there may be a good reason for the lack of progress.
One final thought (I don't know whether it is the same every where), but it would seem that those not blessed with handling skills generally make up for it in airmanship, while those who control the aircraft well see it as the be all and end all (generally the teenage would be fighter pilots).