I think the main factor is that the nationalists get much better and more numerous units at the start. Most of the republican divisions are only 3 battalions while the nationalists are 6, and they also get more of them. The only reason the republicans initially hold is because of the province level debuffs. Once they are gone the nationalist's overwhelming advantage starts telling. Another factor is that the nationalists get both German and Italian volunteers, while the republicans typically get only soviets.
As the soviets, if you want to help the republic win, it's a race to destroy enough nationalist units to even the odds before the modifiers go away. Indeed the anarchist uprising tends to accelerate their fall, but I think the main factor that makes the republicans crumble is the removal of the state modifiers which are the only thing holding them up.