To expand on Forrestfire’s fine answer, berserker strength can be made actually infinite, without having to worry about how much damage you have or haven’t taken. You do that by simply not having enough maximum hp to exceed the threshold. A low Con score, the Frail flaw, the Quick trait can very easily reduce your hp by quite a bit. See our Q&A on “optimizing” for lowest possible hp. Even with the barbarian’s d12 HD, −4 hp/level reduces your expected hp to 2½ × level + 5½, which falls below berserker strength’s 5 × level threshold at 3rd level.
For levels below even 3rd, we can look at rage cleric (Dragon vol. 333), rage monk (Dragon vol. 310), and/or druidic avenger. These all get “rage as barbarian” (though druidic avenger gets it at a modified progression), which means they might be eligible for berserker strength. This is a stretch and a half, really—berserker strength is presented under the “barbarian” heading and makes repeated reference to one’s “barbarian level.” But it is an “alternative class feature,” rather than a variant of the barbarian class itself, and its “level” and “replaces” parameters refer only to getting rage at 1st. If you get that, it might be legit—and each of these classes do. Any of them would be a d8 instead of a d12, so with the −4 hp/level, they expect to be only ½×level + 3½—in other words, at 1st level, 4 hp, low enough to trigger permanent berserker strength.
Even if none of these classes are allowed to have berserker strength, Chaos Rage (Dragon vol. 326) to allow up to 4 non-barbarian levels to stack with barbarian for the purposes of rage, which should work with berserker strength, allowing you to have (at least 4) HDs smaller than d12. If you take a d4-HD class at 2nd, the most hp you could possibly have is 8 hp, less than the 10-hp berserker strength threshold at that level. (And, actually, anything that’s not d12 should work here, on an average roll, though only d4 guarantees you’ll be under even if you roll the maximum hp for that HD.)
Between these, it’s not too hard to ensure that your maximum hp is less than berserker strength’s threshold, making it impossible to leave that state without a Constitution bonus followed by healing (even though the Constitution bonus will bring your hp above the threshold, berserker strength specifies that it ends when you are “healed” above that threshold, so simply being there doesn’t do it, subsequent healing is necessary), or being rendered unconscious or helpless. (I believe temporary hit points don’t affect berserker strength, but the rules aren’t super-clear and you’ll want to check that with your DM.)
The question you should then have is, how do you survive with super-low hp and Constitution? And the answer to that is Ettercap Berserker, a feat from Unapproachable East. Ettercap Berserker gives you +6 Constitution while in a rage, so that’s +3 hp/level for you—and as mentioned above, it doesn’t end berserker strength by itself. Berserker strength only ends if you are “healed” above the threshold. So you can have roughly 8 hp/level—and an OK Constitution bonus for things like Fortitude saves—while maintaining constant berserker strength. If anything does heal you while your hp is that high, berserker strength ends, but that also removes the Constitution bonus from Ettercap Berserker—putting you below the threshold again and restarting berserker strength. This is the basis of my rage cycling build that is discussed in the second half of this answer.