In a comment to an answer, the fellow stackizen Thomas Jacobs said:
Alright. Incidentally, do you get bonus points to your HP every time you level up once you have Morphic Body? Or does it not count because it's an Supernatural Ability instead of a flat bonus to your stats?
(Morphic Body is a Warshaper class feature that gives you a Con bonus while you're not in your natural shape.)
I was going to tell him that it doesn't really matter, because your HP goes up/down when you gain/lose Con but... when you level up, it's important to know how high your Con is because (if negative) it might influence the minimum you can roll on your HD.
I would rule that your Con is your natural Con score, without taking into consideration temporary bonuses from spells, special qualities that are not always active, magic items that can be removed and so on. I can perfectly see how some player who's short on points while point-buying his character getting a 9 Con just to turn any 1 on his HD into a 2 (then later getting a +OddNumber manual of Con).
So, what's the official rule? Which Con bonuses do count and which do not, when calculating your "Min 1" HP gain?