Great comment, Jules, though it's 45 for men, not 35, that's why sperm clinics will take sperm from men up to the age of 45, but not thereafter. Men's sharp drop-off point is 55 versus 40 for women, though if men keep themselves fit and healthy, they can have children indefinitely, as people like Mick Jagger are proving, having children in their 70s/80s no bother. Bernie Ecclestone in his 90s LOL, crazy guys!
It really is about health and fitness, as your grandmother proved, keep yourself fit and healthy and you can have healthy children for as long as you have a biological clock that is functioning, though of course it's complex and there are greater risks, as you mention!
A crazy fact, though there are greater health risks if men are over 45 and women are over 35, those children also have a higher probability of being exceptional. That's the fascinating thing about mutations and genetic anomalies, sometimes they lead to ill health, sometimes they lead to exceptionalism, which means if you increase the probability of mutations and anomalies, you also increase the probability of both possibilities, so exceptionalism or ill health.
That means older men and women having children are more likely to have exceptional children, funny how the world works!
If you're interested, I've talked about the different development rates of men versus women before, though not the latter point, but really interesting stuff all the same:
Thanks for the comment!