My first response to this question would have been similar to Suz, Angie, and Janet, but Rachylou's and Lyn's comments made me stop and rethink.
If "youth" is associated with an "eagerness to keep up with the world" (Angie), "energy and optimism" (Suz), "staying current fashion-wise, as well as music, art, technology" (Janet), then what do we associate with the label "old" --lack of interest in the world, tiredness and pessimism, being stuck in the past, wrinkles, dowdiness, poor health... No wonder we recoil at the thought of becoming "old" and see maintaining "youthfulness" as the holy grail.
Rachylou's comment about associating "youth" with "befuddled, obnoxious, AND also underdone" and "old" with power and command, and, I am going to add, self-knowledge, humility, empathy, and inner strength makes me want to stand up and tell the world that I don't want to be "youthful". Now, I'll agree that these labels are stereotypes and that not all young people are obnoxious and not all old people are empathetic, but really, how did we get to the point where youth gets all the good adjectives and age is left with all the negative ones?
So, at 60+, I'm hereby pledging to do my best to avoid "youthfulness" as I spend my remaining days trying to achieve that state of empathy, humility, strength, and self-knowledge that I associate with age. I'll dress to reflect my pleasure in knowing who I am but also realizing that other causes and interests may take precedent at times and what I wear may not be as important as what I do. I'll take care of my appearance because I recognize that, by doing so, I'm showing respect to those who see me on a daily basis. I'll keep trying to improve and learn and understand the world I inhabit so I can be wiser and more understanding of myself and others. Finally, I'll leave "youthfulness" in attitude, dress, and deportment to the young so that they can enjoy it and then be ready to move on when it's their time to become "old".