One set of weapons from each character has stagger lock. All these weapons have wildly larger stats than the other weapons as a trade off. Use these weapons with characters who you don't employ in the direct use of creating a stagger chain. I currently only have one "stagger lock" weapon and that's on fang who doesn't increase the chain anyway with commando and sentinel. They still "maintain" the stagger, just don't increase it. There's no way around it, they won't evolve out of it.