I had no problems with the Republicans (normal difficulty).
Initially you can use your huge anarchist force in Catalunya, form them into a large stack with the (anarchist) commanders available (Duruti) and move to Zaragoza.
that will prevent any attempt of the overconfident Nationalists there to cut Catalunya off.
In the North (Basque) I organized my units as best as I could, defended, and they held out. They got stronger over time, and eventually counterattacked.
In the South it was chaotic, but the Nationalists did not make much ground. I constantly destroyed the railway lines to Granada.
A counter attack from Valencia slowly gained ground and prevented any success for the Nationalists.
Around Madrid I was getting stronger turn by turn, and when the Int. Brigades arrived I was in an unassailable position. The key here is to not get overconfident and counterattack too early, same as in Basque country.
It could have been a key to hold the terrain at Segovia, to prevent an outbreak of the Francists, As long as they are not through the mountains, Madrid is safe.
Generally the key is not to initially waste the many small units you have, rather keep them intact and build larger stacks.
Eventually, the nationalists could not gain much ground on any of the four fronts, and collapsed when I started massive counterattacks, supported by the International Brigades.
I found it too easy actually, but it was fun all the same.
In reality, the Republic did not lose Madrid, and did not lose the war on the battlefield, but collapsed first because of the loss of the Basque country and - most importantly - because it betrayed the POUM and the anarchists in Catalunya (the civil war inside the civil war), it helps to keep that in mind. Had they fully solidarized with the Anarchists, given them the best weapons, moved the arms factory from Toledo to Barcelona when there still was time, they had a good chance to survive until 1939, when help from France / Britain would have become available.