when I start a client in the stabilization phase, I usually also include some strength exercises that are supported to keep the client engaged. As I observe better control, I add some instability to the stabilization exercises and then watch again to see whether those have been mastered as well. I then phase out some of the stabilization and add more strength endurance but I never really leave the stabilization phase entirely and always challenge my clients with exercises in the category.
To note that I rarely go beyond stabilization and strength endurance because of the kind of clients I have. When a client comes back after an illness or injury. I step right back into that phase again in which I also include MELT and many exercises from the BioMechanics Method.
Hope this helps.
I will usually keep a client in the Stabilization/Endurance phase for about a month. You can usually observe the clients progression in the way they handle the exercises in the workouts you have developed and their ability to handle an increased load. Obviously, some may progress a little quicker or slower than others depending on a number of factors.
After a month, the client may be looking to change things up a bit, so I will move on to strength/endurance. Keep it low key until you feel out how the client adapts. you can then cycle between Stabilization/Endurance and Strength/Endurance depending on the client.