I don't think the article summarizes the research paper well. The researchers gave the AI models simple-but-large (which they confusingly called "complex") puzzles. Like Towers of Hanoi but with 25 discs.
The solution to these puzzles is nothing but patterns. You can write code that will solve the Tower puzzle for any size n and the whole program is less than a screen.
The problem the researchers see is that on these long, pattern-based solutions, the models follow a bad path and then just give up long before they hit their limit on tokens. The researchers don't have an answer for why this is, but they suspect that the reasoning doesn't scale.