I suppose if you are the mentee, this question sounds completely reasonable. But, if you step back, it sounds different. In my years of mentoring people in their professional careers, there has been a common confusion of using the words responsibility and promotion interchangeably. They do not have the same meaning. When you simply ask for a promotion, it comes across as requesting something of entitlement. As if you deserve something. If the mentee changes the question to, "How do I increase my level of responsibility?' it appears they want to have a bigger job and do more for the organization. Sooner or later, all increases in responsibility come with a promotion. If it is not within the current organization, apply the skills obtained to another employer.
So, years ago I started coaching, if you want to rise up the organization, first stop asking for a promotion and start asking for more responsibility. Then:
1) Work harder than anyone else.
2) Do the jobs others are not willing/able to do.
3) Always take assignments in the toughest/most demanding areas.
Mentors - How do you respond to your mentees on these "I want a promotion" sessions?
Mentees - Do you want a promotion or more responsibility?