The majority of lawyers approach a pitch without regard to how well the work is currently being done for the client by the incumbent firm or professional. Even in situations in which they have knowledge of poor performance, most attorneys don't attempt to understand the dynamics of the poor performance. Instead, they pitch indiscriminately in hopes that serendipity and need conveniently converge to win the client's interest.
No one changes providers until they first question the value they get from their current provider. Shaking a client from the comfort of a long term relationship requires that the client see a much higher reward with at least as low a risk as their current provider. Barring that, clients are unlikely to entertain switching from the devil they know to the devil they don't know.
Clients are constantly questioning every aspect of their business. And they value those who help them through this process. If the incumbent provider is not doing this, it leaves a gaping opportunity for a competitive provider to offer this guidance. Develop a questioning technique that walks the prospective client through every aspect of perceived value in the relationship. Your effectiveness in guiding this process is the key to creating the opportunity to present alternative solutions.