The quality or state of being discontinuous; the fact of having interruptions or gaps.
From discontinuous + -ness (noun suffix forming abstract nouns). The -ness creates a noun describing the property itself.
The discontinuousness of human memory—we don't remember everything continuously but have weird gaps and jumps—is why eyewitness testimony in court is surprisingly unreliable.
Complete word intelligence in one call. Free tier — 50 lookups/day.