My cousin and his wife are trying to get pregnant and our question is for the man, does maturation lower the chances of getting her pregnant?

No: Most men are very capable of maintaining there fecundity (sperm counts and ability to impregnate)) into there 7th and 8th decades of life with a big if... The big if, is they must maintain good overall health, be continuously sexually active and avoid heat to the scrotum. if your cousin has sperm concerns he can obtain a sperm analysis easily with a sample at the MD's office or lab.