Uh... no. When you die, you're dead.
Becoming a Nobody is not dying. You lose your heart, but your soul is still in tact. Therefore, according to the rules of KH, you still live. If the Nobody fades (which isn't dying) and the Heartless has been defeated by the keyblade, basically, purified by the keyblade, the heart and the faded Nobody will join together again.
It's not a cycle that is ever continous. After all, how many times can you lose a heart?
And about the Heartless/Nobody thing. Just because you lose your heart doesn't necessarily mean that you become a Nobody. You have to have had a strong heart in order to become a Nobody. And that doesn't even say anything about retaining human form as a Nobody. When you lose your heart, the heart becomes overtaken by darkness- completely enshrouded in it. Eventually, you lose your sense of self (which carries over to the Nobody, along with the memories of the Somebody) and the Heartless basically becomes a killing, heart-seeking machine. You don't control it.
The Nobody, on the other hand, depends upon if you were able to retain human form. While all Nobodies hold to a higher plateau than Heartless, they're still easily commanded.
Except for Nobodies with human forms. They can still think and they remember their times when they were Somebody. Therefore, the Nobody is in control, in this instance.
But no one really wants to lose their heart anyway, so it's not such a big deal which one gets control. It'd all suck either way.