You mean "ubiquitous", not "uniquitous". "A tenuous hold" means you are barely holding on. For instance, you could have a tenuous hold of a rope if you are holding it at the end with one hand and you're almost about to lose your grip. "A tenuous hold on this class position" means they are in the lower middle class and any little thing might drop them into the lower class. For instance, an increase in taxes or the economy getting a little worse or losing a job, certainly. Any small thing like that might drop them out of the middle class. So they have a tenuous hold on the middle class position.

a tenuous hold = a flimsy /shaky/insecure hold