I would have assumed that their influence would have skyrocketed rather than gone down.
In summary: the BGS has a lot of diminishing returns curves intended to prevent that happening, because otherwise every moderately-busy system would likely have its controlling faction pinned to >95% influence.
The basic problem is that:
- bounty hunting without a KWS accrues almost exclusively to the controlling faction; even with a KWS still well over half of it goes to the system controller
- trade and exploration go to the station owner, which especially in systems like Aiaba built around a single major station will almost always be the system owner
- missions are more spread out but not so relevant for a CG system
So as a result, if everything was just linear, the controlling faction would accelerate out towards maximum influence unless there was a very specific (mission-heavy) pattern of activity - and this would be the case even in very low-traffic systems.
To stop this there's two diminishing returns curves in place.
1) 100 actions is not ten times as effective as 10 actions - not even close. So this means that while the non-controlling factions don't benefit from the increased trade, and don't get as many bounties as the controlling faction, they don't end up that far behind on influence points. (This is the main one people think of as the diminishing returns curve in the BGS)
2) Because of how influence adjustments are calculated, 10 actions for a faction on low influence is much more effective than 10 actions for a faction already on high influence. This isn't strictly a deliberate diminishing returns curve - it's an emergent property of other lower-level calculations - but it has the effect again of dampening out influence movements for factions which already have a lot of influence.
So the controlling faction isn't getting that much more (because of curve 1) than most of the non-controlling factions, and the non-controlling factions get much more use out of it (because of curve 2) since they were starting at about 5% influence and the controller was at 60%. And there are multiple non-controlling factions, so as they rise, the controller has to fall.
It will likely not continue forever - as the controller falls and the others rise, the relative effect of the second curve will decrease - and that will eventually form a new equilibrium level, probably before the controller gets dragged into a conflict with one of the other factions.
(Note that the system's Anarchy faction, which won't be gaining any significant bounty voucher influence
and may be getting targeted by "massacre pirates" missions which specifically reduce its influence, is also dropping - not that it started off that high in the first place - rather than rising)