An analog in the human brain is that it can, and does, take micronaps that are not noticeable to conscious awareness, which appears continuous; and it can "black out" for longer periods of time and "come to" with the result that time appears to have suddenly "jumped" (for example, the experience of driving and suddenly your wheels are off the road and you realize you were momentarily asleep).
In short, the gaps are unnoticed. Remember this.
And yet we also know that events which occur at very short lengths of time are processed by the brain just fine, but cannot be consciously perceived.
Not sure I want to agree with the "processed by the brain just fine" bit (it's irrelevant, anyway), but I'll agree that if a stimulus is not present for long enough, then we won't perceive it. Take, for example, a red circle flashed on a screen for one picosecond. I agree that we probably wouldn't perceive it.
So if you were to time the blackouts so that the interval between them were shorter than this subliminal threshold, you'd end up with a series of non-conscious moments even though the brain is working during those moments.
Here's the gotcha point. By your first point, the gaps are unnoticed. So you are not left with a series of picosecond flashes of the red circle with some gaps between them. We are left with a continuous image of a red circle.
But I have to wonder at your assertion that "the brain is working during those moments". This breaks the analogy with single-stepping through the computer program.
You seem to be trying to rest your argument on the fact that the stimulus potential has time to decay during the gaps. In that case, yeah, you'd never reach the threshold to fire a neuron. But this breaks the analogy. It's not at all what the OP was asking about.