Using the Simulation Hypothesis Against Itself
Let’s formulate the simulation hypothesis, which we will call H:

Conscious beings will eventually figure out how to simulate other conscious beings.

When they do so, they will simulate many more of them than ever existed in their universe.

Therefore, if all you know is that you are a conscious being, the probability that you exist in the first, toplevel, nonsimulated universe is extraordinarily small given the fact that the vast majority of conscious beings live in the lower levels of the simulations.
One interesting implication of this line of reasoning is that there are likely to be many levels of this simulation. Conscious beings in the first, toplevel, nonsimulated universe will simulate a universe of conscious beings in the level below them, who in turn simulate a universe of conscious beings in the level below them, and so on.
Let’s formulate a similar hypothesis, H’, along those lines:

Conscious beings will eventually figure out how to simulate other conscious beings.

Every level of the simulation will have fewer resources than the level above it.

Our universe has a finite amount of resources. This is arguably a fact, not a hypothesis, but what is a fact other than a hypothesis which is extraordinarily likely to be correct, so let’s include it.

Therefore, the number of levels is not infinite. There exists a “bottom” level, which will never successfully simulate another level below it.

Each level (other than the bottom) will simulate many more conscious beings than ever existed in their level.

Therefore, the vast majority of conscious beings will exist in the “bottom” level.
Hypothesis H’ sounds perfectly in line with the hypothesis H, since H’s main conclusion was that it’s unlikely you live in the top, nonsimulated, level, which H’ agrees with. H’ just goes a bit further and states that, not only do you not live in the top level, but there is a high probability that you live in the bottom level of the simulation for mostly the same set of reasons. It’s important to note that, by definition, the bottom level will never figure out how to simulate a level below it.
Whether or not we will ever simulate consciousness is highly disputed (in fact, we’re disputing it right now). But if you think that there is a high probability that we will eventually simulate consciousness, as many smart people do, then you must think that P(H’) is relatively low, since H’ implies that the probability that we live in the bottom level of the simulation (which will not be able to simulate a level below) it is high.
In addition, to my eye, P(H) and P(H’) seem to be highly correlated. They mostly rely on the same argument, they just emphasize slightly different aspects of the same conclusion, which is that there is this pyramid of simulated universes in which each level has drastically more conscious beings than the level above it.
So, it seems to me (note the hedging, as this is quite provisional), that the higher you think the probability is that we will eventually simulate consciousness is, the lower you should think that P(H) is (since H’ is evidence against our ability to simulate consciousness and P(H’) and P(H) are highly correlated). However, if we do simulate consciousness, then point 1 of hypothesis H (H.1) is true (H.1 says that conscious beings will eventually figure out how to simulate other conscious beings). And, at least in my opinion, H.1 is the point that, a priori, had the lowest probability of being true! In fact, conditional on point 1 being true, I’d say that P(H) is almost 1 because all the other points in H seem so obviously correct.
To summarize,
Proof by contradiction:
Assume statement SC: It is very likely that we will be able to simulate consciousness.
 P(H’) ≈ 0 because… handwavy math? Ok fine:
 P(SC) = P(H’ & SC) + P(¬ H’ & SC) ≈ 1 (by assumption)
 ∴ P(¬ SC) ≈ 0 (from 1)
 ∴ P(H’ & ¬ SC) ≈ 0 (from 2)
 P(H’ & SC) « P(H’ & ¬ SC) (H’ implies that you’re likely at bottom and can’t simulate)
 ∴ P(H’ & SC) ≈ 0 (from 3, 4)
 ∴ P(H’) = P(H’ & SC) + P(H’ & ¬SC) ≈ 0 (from 3, 5)

P(H) is very small because P(H) is highly correlated with P(H’).
 Also, P(H) is very close to 1 because
 P(H.1) ≈ 1 due to P(SC) ≈ 1 (our assumption)
 P(H) = P(H.3  H.1 & H.2) * P(H.2  H.1) * P(H.1)
 P(H.2  H.1) ≈ 1 and (H.3  H.1 & H.2) ≈ 1 because they’re “obvious”
 ∴ P(H) ≈ 1
Contradiction!
Therefore, it is very unlikely that we will be able to simulate consciousness.
Obviously, the above “proof” isn’t really a proof, and we haven’t found a literal contradiction, but it does feel handwavily correct to me…
“But wait!”, you may be thinking, “I thought this article was going to use the simulation hypothesis to argue against itself, which means arguing that we don’t live in a simulation  not that we won’t be able to simulate consciousness”. Ok, you got me. This doesn’t directly argue against the simulation hypothesis. But, I did say that P(H) is close to one if we can simulate consciousness (SC), i.e. P(H  SC) ≈ 1. And P(H) = P(H  SC) * P(SC) + P(H  ¬ SC) * P(¬ SC). So if you previously thought that P(SC) was higher than you do now, then presumably your new P(H) is also lower, since the weight you’re putting on P(H  SC)  a number close to 1  is now lower.
One last thought. Although I don’t yet see a critical flaw in the argument, I’m not particularly convinced by it either, which is kind of odd. And I’m not really sure why either. I think it’s partly that all these arguments are so counterintuitive and abstract that I don’t really trust myself to be able to spot the logical flaw. But I’ll do my best  so with that in mind…
Potential holes: work in progress
H’ states that because our universe is finite, and each level has fewer resources than the level above it, there are not infinite levels  but this isn’t strictly true. It means that any pyramid of simulations which includes us is finite. The level above us could be infinite. An infinite universe could, for whatever reason, choose to run a simulation with finite resources. It could also choose to run some simulations with finite resources and others with infinite. So you could imagine a branching tree of simulations, some of which are finitely long, while others are infinite. In the infinite chains, there would be no bottom, since infinity doesn’t end. So the conclusion that “most conscious beings will exist in the bottom simulation” would be patently untrue in that case, since the vast majority (or all? infinities are hard…) would live in the infinitely long chains. All that said, if that picture were true, it’d be completely improbable that we’d live in one of the few universes with finite resources, which we do, so I guess it’s probably not true.
I’m sure there are many more holes… will add to this as I think of them.