Since Trade and interaction is essential for long term survival. Those who shun the outside world the most will die the quickest, so I'll give you my top factions to quickly disappear.
0-Enclave Remnants*: Just a bunch of old folks and Arcade, barely counts, if they survive the battle at the dam they only have a few more years.
1-Brotherhood of Steel: Locked in a war with the NCR, Won't Trade with the out side, only makes enemies, won't take on new members, won't embrace reform.
2-The Boomers: Gene pool is getting small and they don't really take in new people (save for that one girl), they will eventually run out of ammo, and then be sitting ducks. Not that open to trade.
3-The Fiends: Just a bunch of druggies, any faction that takes control of the Mojave will wipe them out quickly, very quickly.
4- Cesar's Legion: When Cesar dies, they will fall apart within 5 years, simple as that.
However, the groups who survive the longest are as follows:
1-The Followers of the Apocalypse: They have made a lot of friends out in the wastes. they have quite a bit of tech, and their guards are pretty well equipped. They've made it this far haven't they?
2-The New Canaanites: Sure, their city was razed, like they care.They are clearly capable combatants and though their numbers are depleted they are fantastic traders and love to take on new members.
3-NCR: As the only real country in the whole series, their not going down. They may be crippled internally from time to time, but they are too big and too powerful to die off. They may very well end up re-conquering America, or at least part of it.
4- Great Khans: THE KHANS WILL NEVER DIE! Well, they might, but as long as they don't join the legion and steer clear of the NCR in the future they have a pretty good chance. They trade (drugs) and take on new members, and have good leadership (whether it be Papa Khan or that other guy). The Khans can have a good run.