CVA's not a good example. They did not get kicked out of Providence due to any serious lack in skills or anything, they were kicked out due to absurdly high odds stacked against them at the time.
Few factions these days get the honor of fighting (honest to god FIGHTING) for their home-systems as opposed to just getting squeezed out whenever their larger coalition neighbors deem it prudent, and NO single alliance seem to get the honor of actually fighting without a coalition of their own making it possible.
@ Topic.
When I played, I supported my Faction mechanically by seeing to their interests that a capsuleer can deal with - I ran mission for them, fought pirates in belts, fought player pirates that 'disrupted the peace and harmed trade and commerce', as well as loads of direct involvement in FW from the beginning, with infrequent, but long, breaks.
And here's the important part: Whenever my toon(s) was NOT directly assisting the Federation (or Republic as a proxy of helping the Fed, allies and all that) I made sure I would not be doing anything that directly hindered it or harmed it's interests. Usually by derping in null-sec (presumably being 'neutral' in the help/harm scale) as opposed to anything else.