As the former FA of the Galactic Republic I can offer a little insight into what I personally believe could be the issue. Whenever I was running it, things were easy, wanna know why? I wasn't the only one making decisions. It was me along with, well, everyone who was deciding the direction the faction went in. Now, I have been gone for awhile, but a strange thing I started to notice before I left was everyone was relying on the Faction Admin to do everything. They decided the dominions, the strategies, promotions, gods... there is an endless list of things that was being put on the FA's shoulders.
And guess what that does? It breeds nothing but discontent for the person running the faction. If one person runs the show then, as is natural, someone is going to question their decisions. The thing is, when everyone has input into the direction of the faction, no one can really complain because it is a collaboration. If people do start complaining then you have more people on your side to defend the decisions. It becomes more of a community and less of a "Lets look to this guy for help."
My rule of thumb with running the Galactic Republic was to be more of a mediator instead of the guy making all the decisions. Trust me when I say that this place has a buttload of people with a buttload of amazing ideas. Let them run things, let them make the decisions, no one person can "save" a major faction. It has to be a place where everyone just wants to see it succeed. If you constantly worry about members leaving or people being unhappy with the current rule then... well.... you are doing something wrong.
A good faction just..... does stuff. We weren't worried about the map, or losing planets, or discontent among members. The only thing we were worried about was having a damn good time. We laughed, we joked, we came up with outlandish ideas ( mostly I came up with outlandish ideas ) and the smarter less ignorant people would take that outlandish idea and turn it into something that could actually be written.
Collaboration is key. If your members feel like you are trying to impose your will on the faction you will die as a faction leader. It shouldn't be about YOU as the faction leader it should be about what YOU do for the faction. All eyes are on you, but you don't have to do it alone. In fact, if you do it alone, you are doing it wrong. Share the burden, lets others have the right to come up with ideas, allow people to go out and do things EVEN IF YOU THINK WHAT THEY ARE DOING IS STUPID.
Why did I leave the Republic? Well, it stopped being about fun, and turned into work. We lost our way as a faction and it became more about what everyone else was doing wrong and less about what I can do to fix it. Anyone can point fingers but the real leaders point the fingers at themselves and they fix it. Because I am not above criticism ( And I am as close to one can get to perfection ) so you are certainly not above it.
You want to see the Galactic Republic thrive again? Listen, learn, adapt, be open, and most of all you gotta Wu Tang.