OK here goes.
Remember the timeline stuff? Remember how much the Empire was dominating? I don't think that a few victories for the Republic can counter all that.
I'd bet that the Empire has more raw numbers, more supplies, and stuff.
Yes the Empire ain't doing so great right now, but they're just experiencing a recession. They'll be back (although I'm totally rooting for the good guys).
As for the encyclopedia, I'm sure you're right. But did it say that the Republic was actually doing better and winning the war? Or did it just say that the Sith weren't doing so hot at the moment?