I'm not sure if I qualify as old (just turned 60). But I haven't noticed any changes yet.
I had a scary episode when I was still in my 30's. Has been cautious ever since. I have worked out ways to forestall true altitude sickness symptoms (headache, nauseous). When I fly in, I typically spend the first night at Denver. I tried to do the same even when I'm driving in. But this past summer, I sped through it, all the way from Nebraska to Silverthorne in one day! I was pleasantly surprised I only had minimal symptoms (a very mild headache, which was alleviated with a lot of water. Gone the next morning). But hiking the next day (afternoon) at 10,000' was hard work. Had to stop every 50 yards to let my heart rate drop back to under 100.
The lack of red blood cell for us flat landers can't be helped. It just takes time for the body to adjust. I can't say the adjustment period had changed noticeably yet. I remember panting like a dog just walking up some steps on my first visit to Santa Fe when I was in my 20's! Even back then at that age, it took a couple days for the symptom to go away.
Staying relatively fit helps. It sets the level of activity I "drop from" on first few days at altitude. Thanks to working from home, I was able to exercise regularly with a routine. So me current fitness level is probably better than I had been for quite a long while! I was able to bike/hike at a pedestrian level at Aspen on the second day of arrival. I couldn't climb hill for the life of me. But managed to puddling about the rail trail for something like 30-40 miles. Even managed to complete the bike loop around Lake Dillon (which has a long uphill section, albeit mild grade) on day 3, sucking air notwithstanding...
My friend living in Summit county for much of her adult life is contemplating moving down lower as she gets older (similar age as me). She said it takes longer for her to recover from hard effort, and worse from illness and injuries. I'm not sure that's altitude, or just getting old. I noticed similar age related effect even at sea level.