If everybody's dieing as OTL, Henry VIII would have already remarried following Catherine of Aragon's death. To echo the above posts;
1) For him not to divorce Catherine, she needs to give him a son. Once she dies, you can do what you want with the son, although obviously he needs to die childless sometime for Mary to be Queen.
2) Once Catherine dies, he's likely to remarry almost immediately. Maybe this second wife is childless too, or the children die.
I reckon by the late 1530s he'd most likely marry Mary - be it to James of Scots, or Edward Courtenay, or to a foreign prince. A peaceful end to his marriage with Catherine would likely mean a pro-Habsburg second match to one of her nieces or great-nieces.