Are you sure this is a triad? Because how would taking a break ruin something beautiful for THEM only? If its not working, its not working for all of you. Why are they deciding whether or not this triad continues or takes a break? Why isn't this a three party discussion?
Because if this is them and you on the outside while they continue a facade of calling it a triad - that's pretty disrespectful.
Maybe the break is a good idea and you and A take sometime to discern if there is an actual mutual relationship here. Because if there isn't - why'd they ask for it. Why is she not speaking up about her interest level. Are you interested in HER?