....and a renewable policy until death do you part? The only viable option to staying long-term here is to have an established policy from your home country, that covers you world-wide indefinitely. Not many enjoy such a benefit. Otherwise "Father-Time" will rule you out of the game and you will have to return to your home country.
"O" Visas do not require insurance as of now. But, it's not a good idea to stay here with no insurance. I have coverage from my home country. Otherwise, I would not be here.