Can being hit in the testicles cause fertility problems?

Usually no: Unless there is rupture of the testicle which would be result of severe trauma and cause scrotal swelling and pain sufficient to require emergency room care. These injuries are quite rare, & caused by more than a hit. Ruptured testicles need to be repaired because sperm escaping into the tissue could cause sperm antibodies to be produced which in turn could cause infertility.