My 6yo son has seasonal allergies. 10mg of 24hr Claritin (loratadine) quits working for him after approx 12hrs. Can I give him a 2nd 10mg dose?

No. Don't double up on antihistamines, and refrain from self medicating after a certain point. He needs to be evaluated by his doctor/allergist, check or for an allergist in your area, best wishes best wishes.