Yes, and it used to be pretty common that they would try running again. In recent years, though, it has become unlikely. Losing in the primary is one thing (as Romney lost in the primary, but has gone on to be a candidate in the current Presidential election). But, in the recent past, losing in the general election is a de facto indicator that you are un-electable. That, plus the fact that it is such a gruelling thing (to run for President), most never try again. Look at Bob Dole, Al Gore, Walter Mondale, John Kerry and John McCain.
Harold E. Stassen , former Governor of Minnesota ran for the GOP presidential nomination a record 9 (nine) times . He was never nominated. A more recent NOMINEE who ran once and lost before winning was Richard Nixon.