That reminds me of a old comment on Reddit.

The poster wrote that he got assaulted by a football player, fell on the ground, and somehow hurt his head.

Then he met a girl, they got married after two years and then had a child. Another two years later they had another child. He also had a great job, and bought a house, where he lived with his wife and family for like 10 years.

One day he was sitting on the couch, looked at a lamp, and noticed that the lamp did not look right. The perspective was off. He stared at the lamp for three days. Then he realized that is not a real lamp. Nothing was real.

Then he woke up, still laying on the ground where he had hurt his head 15 minutes ago.

I think the distinction is the subjective perception that time has stretched out a thousand years. It's not that time has literally dilated, just that our "normal" perception of time has changed. Perceived time dilation occurs under certain drugs (to include those endogenous to the human body) and the OP thought has been something that has occurred to me (and others) as well. IIRC, the movie American Beauty suggests it in the last scenes.

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).