Okay, extending the timeframe, what would have been the bar minimum that would have convinced Miliband to try and hang on?
Labour would need to do significantly better than they did in OTL. Scotland is probably the best place for that PoD. You could either have the referendum, but the Better Together side, and Ed Miliband himself, make far less of a cock up of it. The Yes side actually move backward in the polls, and experiences a humiliating defeat which discredits them badly, and the SNP are looking to defend their remaining seats in 2015 rather than take all of Scotland.
But that is difficult to see, so I think it would be easier just to not have that referendum at all, and change the 2011 Scottish Parliament elections, which resulted in a majority for the SNP, so that there is no claim for a referendum in the first place. I am an outsider to Scottish politics, so I dont know what particular factors led the SNP to win there, other than the collapse of the Lib Dem vote it would appear. Perhaps Miliband makes a better first impression on the Scottish public, or Scottish Labour opts for a more popular leader.Or you could go even further back, and change the voting system to be more proportionate when Labour were setting the Scottish Parliament up.
Whatever you do, you'd need to make it so that the SNP win five less seats minimum. They are still in government, but without a majority. No referendum for now. Come 2015, the SNP make gains but not enough to seriously detract from Labour's total to the extent that they actually lose seats over 2010 as they do in OTL.
Come election day 2015, Labour hold onto their seats in Scotland, and make modest gains. What is more the lack of concern over the SNP pulling the strings in a Labour coalition gives them a boost in England too over OTL. Labour get 280/290 seats or so in the new Parliament. Still behind the Tories, but enough to push them into minority territory. The Lib Dems are destroyed as in OTL.
The polls would have to be right too, so 2015 isnt seen as the disappointment it was in reality, and there is a chance that Miliband's fragile confidence isnt shaken, and he thinks he has earned another shot at it. He might get a leadership challenge, but most of the possible candidates are either too close to him to betray him, would have little political disagreements with him, or just dont have the stomach for it, as the likes of Ummuna, Jarvis, and Johnson did in OTL. Maybe you would get a Blairite challenge from someone less prominent, but as we know now, the Labour party is now far more left wing than most people thought, so he would see off the challenger with ease.
Of course, Miliband probably remains unpopular with the public, so we have a similar situation as we are in now with Labour saddled with a leader who the membership like, but the public do not, and a PLP who think he is an electoral liability. Frankly, in this kind of timeline, it would be uncharacteristic of Miliband to stay on, he probably wouldnt have the resolve to battle with the PLP all the time.
The difficulty seems to be with this timeline is making him popular enough that he gains more seats than in OTL, but unpopular enough so that he doesnt make it into government, and Labour remain the second largest party, as surely they would have to to stay out of government with the collapse of the Lib Dems. It is difficult, but I think in this situation there is an off chance of it happening.