I don't have a source, and to a certain degree I must admit I'm guessing. Consider, however, the typical Rhodes Scholarship winner: perpetual scholastic achiever and "grade-getter"; think "Lisa Simpson, if Lisa Simpson were a varsity swimmer." These are not the kind of people who willingly pass up the chance to add to their CV not merely "Rhodes Scholar" but also "M.A., Christ Church [or whichever] College, Oxford University."
I googled around a bit but couldn't find any stats on frequency of degree-getting.
I'd heard that a lot don't graduate because the program of study (if you call it that) is largely self-designed -- kinda like a doctoral thesis. You get your course of study approved by the department and off you go. A lot of students don't follow through and just kind of hang-out & tour Europe for a year (sound familiar?).
By the time they wake-up to the fact that their second year approaches, it's really too late to get anything done. So they leave.
Again, I must emphasize that this is what I've heard. I do not know any Rhodes Scholar, directly or indirectly. If anybody can shed any further light on this one-way or the other, I'd greatly appreciate it.