Maintain consistent ongoing feedback on goals, results and documented career path options.  You must balance constructive feedback with opportunity including training programs to help them succeed to the next level they are interested in.  If you keep them balanced on performance today while setting themselves up for success tomorrow, you will put success in their hands and it is a win-win for both of you.

Another reason people feel they can't grow is that there are not really any jobs for them to grow into.  The key is to let every job evolve.  How can changes in their current job make the company better?  How can the system be improved and what additional responsibilities can they take on?  Teach them new skills and they will feel like they are growing as an individual.  Allow them to develop and implement improvements to the department and/or processes and they will feel empowered.  As long as they know that things will continue to change and evolve, they won't feel stagnant and your company won't either.  You should always be seeking out new and better ways to do things...you employees and your results will benefit.