Subjective perception still requires energy to percept. Thus, to perceive time dilation your brain needs more energy to process it, but there is no a source of such energy.
Fair enough, I see what you're getting at. But I think there is an important distinction: it's not the claim that actual perception goes on forever, but the subjective experience dilates to seem like it. It's quite a bit like the other discussion between the "easy" and "hard" problem of consciousness. You're speaking to the "easy" problem (how neurology correlates to subjective experience), where the "hard" problem is the measurement of how the actual experience feels to the observer.
There is still energy at the moment of death (e.g., your ATP doesn't instantaneously disappear), meaning for a few brief instances, there is still energy to perceive and during these instances, the subjective experience of time may differ from normal day-to-day experience. It's not to say perception actually goes on forever, but the subjective experience of time feels like it does (or, at least changes our normal perception of time).
