If you keep at least one of each potion in your inventory at all times, you won't need to brew any of them. You can just use CopyPasto to replace them.
I have no idea why your potions are disappearing, so I can't help you with that. Try putting them somewhere else, in case it's the shelves that are the problem.
I don't think I've ever tried to brew the Immortality potion but I can't think of any reason it should be any more difficult than the other potions. You could try taking all the potion brewing perks, plus Practiced Practicality, Mischief Master, and Tame the Untameable. That should guarantee success if you brew the potion while you are in the Normal range for Spellcaster Charge.