I'm not aware of any rules that limit number of innings caught. I'm not sure that catching is all that hard on the arm either. It's a lot of throws, but very few are high effort. In HS, my son caught every game, although he'd usually catch only one game of a double header. In summer travel ball, he would usually alternate games with other catchers. Of course this helped get more kids exposure, but it also helped keep the catchers leg fresh so they would be effective at the plate.