Michele Bachmann and Rick Perry both came into the race with momentum. Bachmann has been a leader in some sense of the Tea Party caucus in Congress. Since one of the dominant divides in the Republican party has been between the establishment Republicans (of which Mitt Romney is a member) and the upstart Tea Party, Michele Bachmann entered with some momentum behind her that she may have been the Tea Party's de facto standard bearer in the nomination process. However, her debate performances were simply muted. They didn't contain much of the more extreme positions one might conventionally associate with her that would let her stand out form the field and simply came across as one of the pact. As in, her basic personality in the debates wasn't enough to established her as the clear Tea Party frontrunner and so she fell off in the polls - and so left the first Romney challenger.
Rick Perry arrives next on the scene late but with enormous momentum, overnight jumping in the polls much higher than Bachmann ever had to front runner status given the excitement that he was the only one in the field with the establishment clout (as two term Governor of Texas, ala Bush) to challenge Romney. There are essentially three commonly established explanations for his fall. Firstly, the immigration comments mentioned above. Secondly, a series of gaffes made in the debates such as the infamous "oops" moment when he couldn't remember his talking point of the third department he was going to cut. I am very hesitant to think such minor gaffes have much relevancy. With so many debates, most people don't see any individual gaffe and I think people are usually pretty forgiving of a gaffe if they like a guy and only make a big deal of it when it is used to attack an enemy.
From a policy standpoint, Cain is quite interesting. One the one hand, he heavily promoted his 9 9 9 plan which is, if nothing else, an actual policy that, through concision and repetition, is easily understandable. So Cain might be considered very policy oriented in that supporting him is a little bit equivalent to supporting 9 9 9. On the other hand, outside of this he has been probably the least policy oriented of the candidates and rarely offers much of a substantive policy decision, often hedging his bets by saying things like that he would consult his Generals or his economic advisers without offering an actual policy. That a candidate like him rose so quickly without much substantive policy outside of 9 9 9 indicates one again how a policy focus can be largely irrelevant.
The current (and perhaps the last) runner up to Romney is Newt Gingrich. His rise is clearly very dependent on the timing, but again fundamentally stems from the fact that he came off as very likeable in the debates. This was a guy whose entire campaign staff had quit a couple months earlier and was in the low single digits poll wise. But he stepped into the debates and really shown as clearly the best or second best debater after Romney on the stage. It isn't just that he appears to be intelligent, intellectual even, or other such traits, it is predominantly that he appears to be genuinely likeable. Gingrich is sometimes characterized as acerbic, in a pejorative sense, but I think this attitude comes off more as that beloved no bullshit attitude that says it how it is which is often admired.
Partly because the Republican party as a whole has shifted considerably to the right since Gingrich was Speaker during the 90's (he was far right at the time), and partly because of his personal policy eccentricities, from a policy perspective Gingrich stands out considerably and flies against standard GOP orthodoxy of the day. However, it doesn't seem to matter if the polls are to be believed, which really underscores my view that personality, not policy, is the defining characteristic here.
Ultimately, I would wish that it was indeed policy, not personalities, that dominated election contests. However, it would appear that the driver of polls is precisely the opposite.