Yes, it is reasonable to ask once, politely and without challenging the decision. Some offices give useful feedback, some give only a high-level answer, and some cannot provide anything.
Keep the request short and focused on improvement. This guide on asking for feedback after a consulting rejection gives a good structure for the message.
If you receive vague feedback, do not force the recruiter to become your coach. Combine what they tell you with your own notes from the interview and feedback from practice partners to identify the likely pattern.