It leaves you when you need it most. Relaxation is one component and could be really helpful as an assist in conjunction with other techniques. Yes, relaxation can be harmful if you expect it to do more for you than it is capable of doing. Consider relaxation as one tool in your tool box and use it constructively. If the speaking more fluently approach is used with a client, or the stutter more easily approach is used, or a combination of the two is used, the biggest problem is how much to do and what to do when.
Nothing is as successful as success.
And there is a lot of ice there to melt. In my personal experiences with speech therapy for people who stutter, I have had some very perceptive counselors who I felt did understand my needs at that point in time. In hindsight, if I had the knowledge and the speech pathologist was more perceptive to my needs at that time, ice would have continued to melt at those times. Counseling is a two-way street. I do not write of successes or failures.