This is true in some cases, especially if they don't perceive the value, or they are so cash-strapped that they can't execute on the plans that would really help them.
However, this is often an excuse to avoid having the pricing conversation. I've worked with people who have raised rates on existing clients by 30% without losing any of them.
Usually, though, you'll lose some clients who don't perceive the value and are a giant pain, anyway. You'll get to do better, more interesting work for most of your clients, who will magically start treating you better, and you'll get to do work for a new set of clients who treat you better than the ones you lost.
(Of course, value is not something you assign to a project. It's what the buyer perceives. You can help frame the perception, but it's got to be credible.)
However, this is often an excuse to avoid having the pricing conversation. I've worked with people who have raised rates on existing clients by 30% without losing any of them.
Usually, though, you'll lose some clients who don't perceive the value and are a giant pain, anyway. You'll get to do better, more interesting work for most of your clients, who will magically start treating you better, and you'll get to do work for a new set of clients who treat you better than the ones you lost.
(Of course, value is not something you assign to a project. It's what the buyer perceives. You can help frame the perception, but it's got to be credible.)