I'm 48, in the 5th year of a Marketing PhD. And I certainly know people older than me. I don't think that age itself is a problem. Maybe for some schools, but not in general.
However, there are some other factors that are often related to age. For example, sometimes older people have a harder time getting strong letters of recommendation if they have been out of school for a long time. Or some relevant skills and knowledge may be rusty if they didn't use them for a long time (in my case, I hadn't used matrix calculations for decades so I struggled with that, for example).
It's also good to remember that older people usually achieved higher positions during their careers, potentially with higher salary, status, etc. So, by doing a PhD, they would be giving up a lot, as they would spend years on a lower position with a low salary. On a personal side, older people also have more of a chance of being married and having kids, so the sacrifice the student is making could affect the whole family. Schools may be worried about the toll a PhD will take on an older student.
The statement of purpose and the interview can be critical to convince schools that you are really committed and willing to make that sacrifice, that you know what you're doing. That can be very tricky, I saw some older applicants having a hard time convincing people that they really should do a PhD.
For example, if you say that you had an amazing career in Corporate Strategy and think tanks, professors may think: well, then it's better for you to keep working in corporate strategy and think tanks instead of doing a PhD. On the other hand, if you say that your career wasn't that good, that you are not happy with your career, than schools may think that doing a PhD is just your way of escaping from that, that you want to do a PhD because you hate your career and not because you love academic research.
Another example. Usually, applicants are expected to show they are passionate about research, or something like that. If you are young and already want to do a PhD, that helps to show your passion. But, if you are older and you say you are passionate about research, people will wonder: why did you wait so long then?
So, again, I don't think discrimination is usually the problem with older applicants. But older applicants often have some issues with important parts of the application, like letters of recommendations, skills, and statement of purpose. I see many of them relying too much on work experience, something that is not so relevant for PhD applications. I also see some older applicants trying to sell the idea that what they did industry is similar to what they would do in academia, and that often makes me think they don't understand the differences between industry and academia, and they have no idea what they are getting into. Some applications I see look more like MBA applications than PhD applications.
Now, of course being older also have positive aspects to it. If you solve issues like the ones I mentioned, and bring the positive side of your age into play, your application can really stand out for the right programs. For example, several people told me that my research questions are usually very interesting and relevant. With more experience, it's easier to have more questions and questions that are more relevant.