Even if the stuff you need to finish on a seal is on a non-vaulted destination, the seal will still be vaulted when Beyond Light drops. This is an issue with Chronicler too since most people just need to Truth to Power, hence why there were so many posts about it at one point. You can redo an Ascendant Challenge as many times as you want that week regardless if you succeed or fail. You just won't get additional rewards if you successfully complete it more than once. I would also recommend talking to Toland in each challenge, though I'm not sure if he has anything to do with the emblem.