If 2 Stark characters dies for military claim and as response putting Meera to shadow is cancelled, can it be triggered again because two character died?

Yes. Meera's Response can be triggered one time for each Stark character (other than herself) that leaves play.

So, say you lose a 2-claim MIL challenge and kill 2 Bolton Refugees for claim. Meera responds to Bolton Refugee #1's death and tries to go back into Shadows. The Response is canceled. Meera can then respond to Bolton Refugee #2's death and try to return to Shadows again. This does not violate the "one response per trigger" rule because Bolton Refugee #2's death is a separate and different trigger from Bolton Refugee #1's death -- and Meera has only Responded to each 1 time.

Thanks