As a senior I am wondering if there is a cut-off age for renting a car or if it depends on the agency.
I believe it varies by agency, but for most of the ones we have run into the maximum driver age has been 80.
I think it actually varies by country as well as by agency. You can find a lot of specific information here: http://www.smartertravel.com/travel-advice/know-your-rental-car-age-restrictions-in-europe.html?id=4577096
Let me add that the age 80 max for us has been in Italy.
My father rented a car in Napoli when he was 81. And he drove it over the spine and up to Camacchio near Ravenna and back, by himself. So those who say, ooohhh don't think we should drive in Italy - its spooky, look at what my dad did. In fact, it was this trip of his, funded by the Army, to revisit some of where he was in the War, that gave me the courage to drive to Naples. I've never looked back. Well I digress. In the UK he hired a car at 78. He had to hunt around but he did it. I think he wound up with a local Cotswold agency, in Bourton-on-the-Water. My uncle hired a car here at 81.
If your Dad survived combat in Italy in WWII, it's no surprise a peacetime drive there didn't scare him very much.
It is true, Tom, that he was a Commando in one of the first few. He was in Sicily, Montecassino, Yugoslavia, and finished the War near Ravenna. He was an explosives specialist. Maybe you're right.