It doesn't, even in humans. There is an independent circuit of special muscle cells right on it that keeps it beating.

So starting and stopping the heart in a controlled manner is pretty interesting, because it has to be well-timed, and there are few obvious and reliable inputs to control it, especially when thawing.

Why doesn't my heart keep beating if my brain dies then? Or would it?

I understand that it would keep beating until you are provided oxygen. That’s my understanding understanding of brain death at least.

Probably because the brain controls breathing and so the oxygen runs out quickly

I was going to say that's silly, but I guess we need to be able to hold our breath sometimes.

"Even in humans"- thats a pretty steep assumption.

I am fully aware that if the human heart is severed from the brainstem it will develop A rhythm.

But what about other mammals? Dunno. Not going to assume.

Theres also the tidbit that frogs are not mammals.

The point is that whatever control a frog heart may have, it's not cerebral. It must be a very low-level circuit, which can be modulated from outside, but which remains autonomous.