I hate the fact that a conflict in another system kills the influence in all the controlled systems. And its close to impossible to control.
What i think happens is the effects of the war state is faction wide, so your faction can only gain through combat actions. However, the rival factions in the other systems can all merrily gain from trade, etc. Anyone interested in combat for your faction will flock to the system where the war is active, so your faction generally suffers in the other systems whenever there is player activity present.
But without any player activity, there shouldn't be any change at all to your faction in any systems, including the active war one. This rule should apply to any states other than expansion and retreat. Also there can be small adjustments queued from previous ticks, but this is usually only 0.1% or so.