Diehard keeps you upright and able to act instead of being unconscious when driven to negative hit points. But to be honest, how often are you at this point? If it happens a lot, then maybe it'll be useful. But it would be more useful to find ways to avoid going negative to begin with, such as better AC, miss chance, improving your offensive abilities, etc. Also, at high levels, a monster can take you from a positive hp total to dead and skip over that range from -1 to -Con score. My character got ripped apart 2 sessions ago by a glabrezu that did just that, driving me from about 40 hp to -25 with a couple claw attacks and a rend. Think carefully about this choice, as you'll have to use a feat on Endurance, which is not often useful, then get Diehard. Do you really want to do that just in case you need that divine intervention that acts like a 15th level cleric's heal?
I second Lathiira's post.
When you actually have over 150 HP, you'll be fighting some nasty stuff. Stuff that can do 100+ HP damage to you in a single round - and frequently will.
If you're sitting at 90 HP and take 100 damage, you'll be glad you had this feat. If you're sitting at 110 HP and take 100 damage, you will wish you had taken Dodge instead (for example). And if you're sitting at 80 HP and takk 100 damage, you'll just be dead.
And if you're sitting at 1,000 HP and get hit with a Dominate effect, you'll wish you had taken Iron Will and Improved Iron Will.
How often will Endurance/Die Hard really help you?
And don't forget, if you're in combat, and something whacks you with an axe down to negative HP, then taking that potion out of your pack provokes an AoO, and drinking it provokes another AoO. If you're at negative HP and get hit with an AoO, you're gonna die for sure. So what will you do? Spend one round withdrawing and pray that the monster attacks your wizard friend instead of you (it could just follow you to wherever you withdrew and then attack you there and finish you off). If you live, you can spend next round drinking your potion while you watch your wizard friend die. Then the round after that you can rush back into combat.
Side note: Unless you're holding a two-handed weapon, you will probably also need to sheathe your primary weapon and then draw it again after you drink the potion, which puts you into the 4th round before you are back in the fight.
That's a three-round (or four-round) solution that includes having to resurrect one of your allies.
No, saving yourself in melee with a potion is a losing strategy in the first place. 10x more true when your HP are already negative.
Instead, take feats to get out of the way of the damage. Iron Will can keep you in a whole lot more fights than Diehard. Lightning Reflexes will help you hang onto your HP longer. Dodge and maybe even Mobility will go a long way toward avoiding damage, especially if you're a fighter. Take Toughness if you haven't already - having a positive HP total is more important than remaining active at negative HP.
And finally, take feats to kill those big nasties before they have time to whack you into the negatives.