That's not always true. Sometimes people end up unmotivated because the organization shifts its mission in one direction while they shift their values in another, and so what starts out as great mission-alignment falls out of alignment. Sometimes people grow out of a role when the role doesn't grow with them. Sometimes peoples' life circumstances change and they don't have as much attention to devote to work. Sometimes people are just looking to collect a paycheck and don't care about the work at all.

A manager should always start by assuming that a motivation problem is something he can address, and work with the employee to figure out what the real reason is and see if they can make the necessary changes. But sometimes, the employee and organization just aren't a good fit anymore, and it's better for both of them if they part ways and find new situations that are a good fit.