I'm a stutterer. As a child a could hardly finish a phrase with out getting stuck on a word. I distinctly remember being ridiculed for the way I spoke. I think about 2nd grade I discovered that I could tell when a word was going to be trouble. I would try to pronounce the word but if I could not get it out in one try, I would stop, think, and replace the word with a similar meaning word. If I couldn't think of a word, I would replace the phrase and move forward. At times, it was a bit awkward but most of the time it was no big deal. Trying to fight through a trouble word is next to impossible so it's just easier to replace it.
As an adult, I do the same thing to stop my stuttering but it's gotten way easier to find a replacement word. I still have trouble when I get nervous but I have to remember to slow down. I don't think any one notices or cares that I've slowed down so it's worked for me. I also find myself previewing what I will say in my mind before I say it. So I usually don't say something with out thinking it first.
I don't think stuttering can go away for everyone, but for some it does go away, but it's something you can manage. I never had speech sessions but I suspect that a few hours a week is not enough. In the past, I had to constantly be aware of what I was saying and making sure I practice my word replacement. The more I did it the easier it got/gets.
I don't think anyone knows that I'm a stutterer now. I do a good job to over come it. I think it helps to know that it is something that can be managed. It's just something that you need to constantly try to over come.
I feel for your kid since I know what he is going through and what he will face. I also know that it can be managed so I think you'll need to work with your four year old, now. You need to constantly help him to make sure he understands what to do when a word is a problem by having long conversations with him to help with what he needs to do. Good luck!