4. Let's Kill Hitler
In the first episode of the second half of series six, Amy and Rory's friend Mels essentially TARDIS-naps the dynamic trio and takes them back in time to 1940s Germany, where they crash into Hitler's office, accidentally saving him from a premature assassination. Hitler shoots Mels, killing her, and she regenerates into River Song (whom the trio learned one episode previous is Rory and Amy's daughter). River immediately succumbs to the brainwashing of Madame Kovarian and the Silence, and begins trying to kill to Doctor. Ultimately, she poisons him with a kiss; the poison will not only kill him, but prevent regeneration as well.
When He Should Have Regenerated: River, after realizing what a good man the Doctor is, and who River Song is (due to her and the Doctor always meeting in the wrong order, she is unaware that River Song becomes her alias at the beginning of the episode), she gives him all of her remaining regenerations to stop the poison and keep him alive. Because the Doctor is so close to death, and he was protesting what River was doing, he likely was unable to control the energy himself. That much regeneration energy flowing through him should have sparked a regeneration. River, likewise, showed no ability to control regeneration energy earlier in the episode (other than jokingly saying that she was concentrating on a dress size), so it can be assumed that she too didn't have the ability to control what the energy did once it was inside him. With the addition of John Hurt as a previous incarnation of the Doctor, and Peter Capaldi about to take over as the next incarnation, the Doctor will, as of Capaldi, be in his thirteenth and final incarnation. Moffat has previously stated that the BBC would come up with "something" when the time came to make way for more regenerations, and a recent interview at the Chetlanham Literature Festival, said, "I think you should go back to your DVDs and count correctly this time. There's something you've all missed." Some people hypothesise that River's gift of her own regenerations are what he's referring to, and if that turns out to be true, perhaps that explains why they didn't want to force him to regenerate in this episode.