My thoughts were that when A is split across three independent groups the group sizes change (ie get smaller) so the 'effect' may not be as statistically significant. Also does the effect A seem more prominent in only 1 or 2 of the independent groups, so when you split it between 3 groups the significance changes.
However, just to add I am not a statistician and as it is early, my effective caffeine intake has not been reached yet :p