Hi OP,
When your minor faction controlls X systems, where X is a number at least bigger than 30 (given PP affects lots of systems at a time) - ok 30 is my speculation, there is a chance. We will actually get more details for 1.4 according to the recent dev diarny, so watch out for them to see what needs to be done.
I will disagree with some, Powers do affect the background simulator for exploited and controlled systems. I have a civil war to fight this week to prove it due to a -50%-ish influence drop at the resolution of the pp cycle, because of late fortification. Basically different powers can convince different sorts of governments and arne not so good against others. They do not like controlling minor faction with different major power allegiance. Mahone is our controlling power, so obviously Alliance and strong against Corporates. Alas my chosen minor faction is a Federation Corporation, so we get large influence swings because of PP.
You are doing very well to get your faction to 90%. I think 96% is the largest influence you can get, and you can see why a 50% swing with one other faction gaining can be very annoying. At 90%+ your faction, will be considering expansion. There are 2 things I can think of that could be happening, if it keeps dropping.
1) Powerplay is degrading your influence as the controlling power does not like your controlling minor faction.
2) There are not sutaible systems to expand to or you have expanded, anbd not noticed!
For (1) if the majority of your swing occurs Tuesday/Wednesday this is the likely cause (fortification and opposition tend to go up most those days). To double check, if in the system map or in starport services it s says "exploted by" or "controlled by" and a power name IN COLOUR (just to rub it in). Then pp is having an affect. In system map if you are a single star system (sometimes if there is more), system map will start with the physical details of the start, press left+right mouse and move up and down until the system overview comes up. Factions and states come up. Be warned if the state is blank, it means a faction is in an "Election" conflict.
For (2) a faction can expand to a system that has fewer than 5 factions if it is within 20LY. Your faction may well have expanded. When expanding, take a look around. When expanding the faction will have a state of expanding on the system overview on the system map.
The Lugh/CSG threads from around 1.1 time are a really good source of info about how to make a faction the controlling faction in a system and to expand it.
Simon