As a consultant, I've had opportunities to take my BA career in a variety of directions over the years. And I've seen many different career paths at client sites too. I've also found it necessary over my entire career to switch companies (and to switch between employee and consultant roles) to build experience and skills I wanted. I've seen BA paths that remain on the requirements definition and management side, or move into PM or Program Manager roles, or move into general IT management, as well as BA team leads. Consulting gives other opportunities to focus on strategic planning, business / solution assessments, etc. - those are areas that I've found most interesting and have been able to make the focus of my career over the past several years.
My career has moved from systems analyst to PM to senior BA to Business Architect. As Chris noted, there are some key skills needed in this path that require more breadth across the BA skillset. 'PM' skills such as people management have not been most important in my career - other skills including strategic planning, working at the executive manement level, business process design and business re-engineering have been most valuable. Roles such as BA team lead within projects have given the people management side without a specific PM role.
As far as certifications go, I am actually pursuing TOGAF certification rather than CBAP as a Business Architect. But I continue to actively support IIBA and BABOK in standardizing and building the BA profession regardless of career path.
The best advice I would give is to actively look for and take advantage of opportunities anywhere you can find them - dont' wait for them to be officially given as part of a role, and try not to limit to just one path or option. Even if you're not exactly where you want to be right at this moment, try to find any chance to learn something new and go for it. You've probably already acquired a lot of skills that you hadn't really planned to acquire - and with luck, that will never stop happening no matter where your career goes.