Countries where the same leaders run, even after losing

[Niemeyerite]

No one mentioned Lula.

Oh, and that's the rule in Spain. The only President who's never lost an election is Zapatero (Calvo-Sotelo doesn't count). But Suarez, Gonzalez, Aznar and Rajoy have run and lost at least once.

[Peter the Lefty]

This is the norm in Israel, In fact this even happens after a PM resigns because of a scandal (Rabin) or losing the confidence of parliament (Barak).

Oh boy, let's see here.  Begin lost in 1949, 1951, 1955, 1959, 1961, 1965, 1969, and 1973 before finally winning in 1977.  Peres lost in 1977, 1981, and, depending on how you look at it, 1984, not to mention 1988, and 1996.  Netanyahu won in 96, lost in 99 and 06, and won again in 09.  Anyone else that I'm forgetting? 
Also, in Greece, George Papandreou lost in 2004 and 2007 before winning in 2009.  Kostas Karamanlis lost in 2000 before he won in 2004.  Andreas Papandreou lost in 74 and 77 before winning in 81.  Of course, let's also not forget the Andreas Papandreau/Constantine Mitsotakis duels. 
Italy: Berlusconi won in 94, lost in 96, won in 01, lost in 06, and won again in 08.   

[○∙◄☻¥tπ[╪AV┼cVê└]

In the U.S. if you run for President and lose, you don't run for President again. At least as a Democrat or a Republican.

Nixon was the last guy to pull off that move, after waiting a cycle.

In Mexico, AMLO just barely lost, again. I don't know if another PD/PT Candidate could have won there, but it might be worth trying to avoid putting the same loser up over and over....

McGovern lost the nomination in 1984. He got 3rd place in Iowa. The Democrats decided it was time for a new 49 state loser.

Bush didn't have a real win in 2000, but ran again in 2004.

William Jennings Bryan probably finds this thread hilarious.

Honorable mention to FDR. Let's see. You're a Democrat running for VP, and you lose your home state of New York by 40 points? Well, clearly you're destined to win the Presidency 4 times after you get polio.

[ag]

You can emerge moral victor / unscathed / still viable from a lost primary campaign in America, not (anymore) a general election.

One hasn't, but it doesn't mean that one cannot. It's too small a sample to make any conclusions of this sort.

[The Mikado]

This is the norm in Israel, In fact this even happens after a PM resigns because of a scandal (Rabin) or losing the confidence of parliament (Barak).

Israeli politicians never go away unless they die.  Shimon Peres has been something or other in Israeli politics for over three decades now.

[Simfan34]

I really want to see a Sarkozy comeback.