Well, considering it's the same Republic of the Clone Wars, they essentially have to win every war that would otherwise result in their dissolution.
It's actually not the same.
About the only thing they have in common is a name and they hold the same 'land', to an extent.
There were fundamental changes made to the Republic after the Dark Ages.
1. The Empire could rule for a time, like 50-500 years, then get over thrown. It has happened before, or it will as the case my be.
2. Eventual Republic victory doesn't have to be immediate. The Hundred Years war lasted for over a hundred years with ups and downs before France won.
Wars don't have to end over night in SWTOR.
And as an Empire player it is pretty dam annoying to have all of my achievements ignored or undone by the Republic. It doesn't help that the new novel all but says that the Empire is on it's last legs and the Republic is on the short road to victory.
So yay for me look at all I accomplished.