If it didn't happen, it's amazing how much effort climate scientists put into explaining it. With enough parameters you can always make the theory fit the data. With enough judgement calls on estimating the data, you can almost always make the data fit the theory.
I don't have an explanation of the mechanics of the pause, although I've seen some candidates. But the pattern looks pretty clear if you look at global temperature for the past century+. It looks like a rising line from AGW with an oscillating term superimposed with a period of about sixty years. That gives you thirty years of rapid warming from about 1911 to 1941, thirty years flat to cooling until about 1971, thirty years rapid warming until about 2001, then again flat.
I don't have a model, although the obvious guess is that it has something to do with atmosphere/ocean interactions. But considering that the IPCC with its models has, on average, done worse at predicting warming than a straight line extrapolation of the trend from 1911 to the first IPCC report, extrapolating the past pattern seems like a reasonable approach. If it's right, the current pause should last until about 2031, followed by a renewed period of rapid warming. Whether the current AGW orthodoxy can survive that long I don't know.
My serious critique of the current orthodoxy is on the consequences of climate change, not the pattern, but the above strikes me as a reasonable guess at what's going on.