An impasse is a reason (from the speaker’s pov (point of view)) that the discussion isn’t working.
Impasses take logical priority over continuing the discussion. It doesn’t make sense to keep talking about the original topic when someone thinks that isn’t working.
An impasse chain is an impasse about a discussion of an impasse. The first impasse, about the original topic, is impasse 1. If discussion of impasse 1 reaches an impasse, that’s impasse 2. If discussion of impasse 2 reaches an impasse, that’s impasse 3. And so on.
A chain of impasses is different than multiple separate impasses. In a chain, each link is attached to the previous link. By contrast, multiple separate impasses would be if someone gives several reasons that the original discussion isn’t working. Each of those impasses is about the original discussion, rather than being linked to each other.
When there is a chain of impasses, the most recent (highest number) impasse takes priority over the previous impasses. Impasse 2 is a reason, from the speaker’s pov, that discussion of impasse 1 isn’t working. Responding about impasse 1 at that point doesn’t make sense from his pov. It comes off as trying to ignore him and his pov.
Sometimes people try to solve a problem without saying what they’re doing. Instead of discussing an impasse, they try to continue the prior discussion but make changes to fix the problem. But they don’t acknowledge the problem existed, say what they’re doing to fix it, ask if that is acceptable from the other person’s pov, etc. From the pov of the person who brought up the impasse, this looks like being ignored because the person doesn’t communicate about the impasse and tries to continue the original topic. The behavior looks very similar to a person who thinks the impasse is stupid and wants to ignore it for that reason. And usually when people try to silently solve the problem, they don’t actually know enough about it (since they asked no clarifying questions) in order to get it right on the first try (even if they weren’t confusing the other person by not explaining what they were doing, usually their first guess at a solution to the impasse won’t work).
This non-communicated problem-solving attempt problem is visible when people respond at the wrong level of discussion. Call the original topic level 0, the first impasse level 1, the second impasse level 2, the third impasse level 3, and so on. If level 3 has been reached and then someone responds to level 2, 1 or 0, then they’re not addressing the current impasse. They either are ignoring the problem or trying to solve it without explaining what they’re doing. Similarly, if the current level is 1, and someone responds at level 0, they’re making this error.
The above is already explained, in different words with more explanation, in my article Debates and Impasse Chains.