First off, you have to realize that there are people in every age group who also have gotten numerous rejections..that have the same numbers and stats that you do.
I think youth, in some cases, can hurt in the admissions process. Similarly, I think being 'older' can hurt as well. It depends on the applicant, their experiences, the interviewer, the adcom, etc. I have heard that UCLA and UCSD are pretty stingy when it comes to accepting older applicants. UCSF, on the other hand, has atleast 10 students who are over thirty, and a great deal who hover somewhere between 25 and 30. 70% of our class has taken atleast one year off from college. With this in mind, I don't think that a student will ever be rejected because of their age. I do think that a person could be rejected because they are thought to possess little empathy, maturity, or other characteristics that are incredibly important in the profession of medicine. The lack of these qualities, however, can occur in any age. Some schools do appear to favor traditional applicants, while others tend to favor non-traditional applicants. In the end, I think age doesn't matter all that much.
I will say that, being 28 myself, I am very glad that I am in a class where there are many other students who are in my age group. I've heard that many people love medical school b/c it is like high school again. I find that being my age it is hard to share in that kind of enjoyment, however, I do appreciate the opportunity to form close bonds with many people that I find a deep connection with as I focus gaining the skills and experiences necessary to serve my future patients. I am really enjoying my opportunity to become very close to some of my classmates whose ages range from 22 to 36.
More and more there is a consensus growing, among some medical organizations, that medical students and residents are progressing through medical school and post-graduate training, but are doing so with poor bedside manner and marginal communication skills. I think that when it comes to these qualities the 'older' students may have a slight advantage (sometimes, so please take a breath before flaming). There are some young, traditional students who are great, but I think that the proportion of older students that are comfortable dealing with very intimate and personal issues is higher than the proportion of younger students. There is something to be said about 'real life experiences', even if they are only for one year.