Ability comes & goes but talent never leaves you, I play with 2 Ex Scottish International golfers at least once or twice a week both have done a stint on the tour, one of them is 62 & the other is 65. Both still play of scratch and can knock it out there 260-280 of the tee and have a short game to die for, so if you put the time in then you can go on for years.
They both have active handicaps and continue to play & Practice every week.
I you have a good swing that does not put any excess pressure on your body and you keep in shape who knows. I use to play with an old boy years who was 68 and playing off 4. He had shot below his age nett and was positive that one day he will do it gross. He had a lovely swing and was a fantastic golfer, but he looked after himself and kept in good shape.
the answer lies partly in the Tour's line in the sand -> Champions Tour, but in practice it's probably a touch below that line.
doesn't mean you will get worse of course, so many other factors come into play when you look at any amateur golfer, but there does seem to be a correlation between how early you learnt (and got your low handicap) and how long you can go on playing to a good level. Logically this would be because your capability is developed outwith your developing physical capabilities; so you are less reliant on them. Most 65 year olds are as strong as a 15 year old
Mines is slowly going and Im only 24.....creeping upwards and upwards! Theres a lad not much older than me was off 3 as a junior, club champ etc, went up 0.1 consecutively to 8 or 9!!!!
Member at my place took up golf when he was in his late 40's and got down to 3 in his 60's. He won the English 65-69 age group Championship a few years back. Over 70 now and still off 4.
A very good question and there's no defining answer. Fitness, attitude, golfing prowess, equipment - all will play a part. However there's no doubt that improvements in golf technology has been of huge benefit to mature golfers as they can now play the game to a high standard and for much longer than they could say twenty years ago.