Of the other 31 state legislative recalls, I only know of one, the 1914 recall of Edwin E. Grant of California (see the link for more details on that bizarre race -- this post is very similar to the the earlier post) was a rerun. I don't know the details on some the other races, and the Michigan replacement votes take place months later, so huge asterisks on those.
I haven't done a full search on the 151 recalls from last year, but I think there were only a handful (I see this one) There have been a few noteworthy ones including these two. But it is still unusual. The more prominent recalls were not reruns.
That’s not to say that losing candidates don’t think of it all the time. After the bitter 1994 Senate election battle, Michael Huffington allegedly wanted to try and recall Dianne Feinstein. As you can see in this story, it was quite temporary. It could be argued that Richard Riordan’s desire to get into the 2003 recall (which was short-circuited by Schwarzenegger) was also a “second bite of the apple” (Riordan lost the Republican primary in an upset in 2002), but Riordan didn't win the primary and didn't end up running in any case.
Why doesn’t the rerun happen more often? It is not that losing candidates are chastised. Many losers go back to the well repeatedly. On the national level, in the days before primaries, we use to see the parties regularly renominate losing candidates, like Henry Clay,William Jennings Bryan or Adlai Stevenson (who almost invariably lost the race again -- Grover Cleveland actually won a majority of the popular vote, but lost the Electoral College in 1888). The Republicans are known to choose their runner-up in the last election for their candidate (something that Mitt Romney is counting on).
It is also not because voters don’t want to legitimatize a “naked power grab.” Voters have clearly been willing to endorse a strictly political recall that is run simply to benefit one party.
Let’s hypothesize (and your guess is as good as mine). One reason: the candidate may appear to be a sore loser who is trying to reverse, at the public’s expense, a legitimate election vote against him/her. It can easily be seen as, or more likely turned into by the incumbent’s judicious campaigning, a personal vendetta. On a practical front, the opposition research has already been done by the sitting elected officials, and the incumbent already knows the dirt to use.
Another powerful disincentive is that voters may see it as hijacking the voter anger (and the volunteer efforts, if any) of the recall for personal gain. Witness Congressman Darrell Issa, who ponied up the dough that got the Gray Davis recall on the ballot, but abruptly dropped out as more popular candidates came in.
Issa also points out the third possible negative repercussion of having a rematch. It gives the incumbent something to hit. The recall suddenly becomes a straightforward political race – it is no longer just about voter anger or a diffuse electorate. The elected official can present ads against the alternative. That Issa was the face of the recall did not help him. He had started to come under fire before he left the race.
None of these reasons are enough to prevent a good candidate from coming forward in a race -- and let's not forget that Barrett came close to winning in a terrible for his party. Clichés abound in politics and one that is especially true is that you have to be in itto win it. But the paltry history of recall rematches suggests that there are good reasons for losers to shy away from getting involved in a recall. We’ll see what happens with Barrett.