Three POD's for you to consider.
1) 1931-33 the new Republican Governement manages to make fewer enemies, perhaps being conciliatory with the church or working better with progressive elements in the army. Also it deals with land reform straight away thus removing some of the agrarian violence. Thus when the coup comes the army has less of a base.
2) Outside Spain the depression leads to left wing revolutions in Germany and other European countries. This removes the Nazi/Fascist intervention allowing the republic a more level playing field. This could lead to a Spanish left revolution. (Personally I think this is all very unlikely)
3) 1936. The actual rising was a very chancy affair and some of the cities taken by the Nationalists, (eg Oviedo, Seville, Zaragoza) could have turned out very differently, (I have started to explore this in my timeline that is linked to my signature). Change a few of these and you could have had a longer lasting republic.
I am not going for the bonus points for the CNT/FAI areas lasting. IMHO, they only flourished because of the revolutionary situation and the weakness of the republican govt post the coup, (not that it was particularly strong before) and that weakness was one of the major reasons that the republic never really was able to get to grips with the situation once the generals rose. So therefore their very existence is evidential as to why the republic eventually lost. That's not a value judgement on them as entities but a hard nosed political reality.
