This might be a more technical and non-judgmental (“love him”/”hate him”) answer than you would like, but in the study of strategy, there are two ways to answer this question. I am only going to offer one because it deals specifically with the nature of strategic “peaks”. The other answer deals with stages of a campaign. I will write another answer on that if someone specifically asks about where Peterson is in his campaign.
To understand the nature of Peterson’s situation, we discuss “stickiness”, one of the six benchmarks we used to evaluate strategic positions. The term “peak” applies to the most “sticky” positions. Positions are sticky when cannot leave these positions without surrendering major element of the position. However, it is also very difficult for anyone to dislodge anyone from these positions.
The analogy is a mountain peak. It is very difficult to attack uphill. These positions are easy to defend. By this definition, Peterson’s position has proven to be very sticky. He has been broadly attacked in the media and in academia, and it has only built up his position, Therefore it is a peak. It is difficult to imagine an attack that hasn’t been tried, so it is difficult to imagine one that would work.
Continuing the mountain peak analogy, however, stickiness has a downside, literally. We cannot move from a mountain peak without going downhill. Peterson's position sits upon a mountain of work. He would find it very difficult to disavow or move away from some major element of that work. He must defend because he cannot abandon what he has done and move to a totally new position.
However, peak positions can be built up higher and expanded outward. Those in peak positions can find more and more advantages to their position, building up their mountain and extending their control over it. We see this in all companies with peak positions: Coke, Apple, Amazon. All have been spanked for trying at one time or another to move away from their position, but they do great when they build on it.
If you mean by “peaked” that is it all downhill from here for Peterson, that seems unlikely. Peak positions tend to last a lifetime unless they are abandoned. Some have more upside than others, but that depends on the vision of the person that commands them. He could make a mistake, but, by their nature, sticky positions tend to prevent people moving away from them. Even when they want to.