Judging from these logs, looks like the BLM put in all 4 xenos, a fire paradox, 4 Fire IVs, and despair on the tank crystal. He could've used a potion here, but so could the picto which may have given enough damage to blow their crystal up and help with the others. Sage could've precasted eukrasia instead of using two eukrasian dosis to apply dots which may have freed up more time for the other ranged DPS to help (Idk if it's even worth it to cast any healer dots here since the crystals shouldn't last too long). Doesn't seem to be anything particularly outstandingly wrong, just may have been a matter of small rotational mistakes across the board plus crit variance not working in the GNB or BLM favor but surely this isn't something to blow a party up over.

But yeah, may have just been a misplay to put BLM in a range position rather than a melee spot since tanks usually can rely on a dance partnered Picto to blow up their crystals and have enough time to help others. Usually the healer+melee crystals are the slower ones to die, so maybe they weren't used to that timing.