I'm not quite sure what you mean, but if you can't reduce the size of your position without losing your shirt, you're not really winning; and if staying in your position requires you to put up more money than you can raise, you've hit the limit I was referring to. No one can expect to keep finding money to support their trades until they turn profitable.
EDIT: Maybe you mean that they didn't try to make a larger bet after they got in trouble? But whether they needed to make a bigger bet or whether their existing bet was already too big, it's still the same issue; the only way to avoid liquidation is to expand the use of credit, which hits a limit at some point.
I interpreted your comment as an allusion to the probablistic fact that, given an infinite bankroll, you can exceed any profit, in time, betting on coin flips.
I tried to point out that LTCM had a very reliable and profitable trade on the basis anomalies they identified, which, combined with their imprimatur and aggressiveness, enabled the leverage that enabled them to dig their own grave (they ended up with nearly the same leverage as Lehman).
I worked on a team with OG LTCM and Lehman MBS quants, and they had some very interesting stories parallel to the standard narratives you hear about these events.
Seeing that he worked with some LTCM quants, I would imagine he knows more about the situation than you do. The kinds of ineffiencies LTCM were exploiting made sense, it's just during times of stress the historical correlations between pairs start to break.
But, hey, I'd bet on coin flips all day long if I was given favorable odds.
I don't know, the "it's just" part kind of indicates that the real probability of things remaining correlated were not what LTCM thought they were, to the point where they couldn't afford to stay in the position long enough for things to snap back. I don't buy that as "always winning".
EDIT: Maybe you mean that they didn't try to make a larger bet after they got in trouble? But whether they needed to make a bigger bet or whether their existing bet was already too big, it's still the same issue; the only way to avoid liquidation is to expand the use of credit, which hits a limit at some point.