My focus here is on pointing out that "multiple-time" Democratic seekers of the presidency - since the Civil War - have not fared well.
If you ran for the office and lost once (regardless of whether or not you obtained the nomination), your second (or third) run did not end in winning the presidency.
My point is that Democrats have had electoral success when nominating people who have not sought the presidency previously.
Let’s look back at multiple-time Democratic candidacies since the post-Civil War era. I will try to avoid "favorite son" and “eccentric” candidacies but this list is not meant to be exhaustive.
General Winfield Scott Hancock – candidate in 1868 (lost to Seymour at the Convention) and 1876 (lost to Tilden at the Convention), finally received the nomination in 1880. Lost in a fairly close election to James Garfield.
Thomas Bayard. Lost at the Convention in both 1880 and 1884 (to Hancock and Cleveland, respectively).
Williams Jennings Bryan. Three-time nominee, lost to McKinley twice (1896 and 1900) and Taft once (1908) in the General Elections.
Alfred E. Smith, lost at the Convention in 1920 (Cox) and 1924 (Davis) and in the General Election in 1928 (Hoover), and again at the Convention in 1932 (FDR).
Richard Russell – lost at the Convention in 1948 (Truman) and 1952 (Stevenson)
Adlai Stevenson – twice the nominee (1952 and 1956, lost to Eisenhower both times). Lost the nomination in 1960 (JFK).
George Wallace – best known for 1972 and 1976 but he also entered some primaries in 1964 (most notably Wisconsin). Failed to secure the nomination all three times.
Hubert Humphrey – 1968 nominee – failed to win the nomination in 1972.
Eugene McCarthy – fabled 1968 campaign, ran as a Democrat in 1972 and 1992 (the latter was not serious), also as an independent in 1976. Never won a Democratic nomination or general election.
Scoop Jackson – failed to get the nomination in both 1972 and 1976.
Jerry Brown – ran in 1976, 1980, and 1992. Didn’t win the nomination in all three attempts.
George McGovern – nominee in 1972, didn’t come close to getting the nomination in 1984.
Fred Harris – ran for the nomination in 1972 and 1976, no success in either cycle.
Terry Sanford – sought the nomination in 1972 and (briefly) 1976. No luck either time.
Gary Hart – ran in 1984 and 1988, close the first time, a dismal showing the second time for reasons many of us will remember.
Jesse Jackson – ran in 1984 and 1988, basically third behind Mondale and second behind Dukakis.
Al Gore – 1988 and 2000. Nothing else need be said about the second run. That almost broke the pattern.
Dick Gephardt – 1988 and 2004, didn’t win the nomination either time.
Dennis Kucinich – 2004 and 2008. Distant showings both times.
John Edwards – 2004 and 2008. Ugh.
So – based on the track record, it is fair to ask what this means for Joe Biden (1988, 2008), Hillary Clinton (2008, 2016), John Kerry (2004), Martin O’Malley (2016), Lincoln Chafee (2016), or even Jerry Brown (1976, 1980, and 1992) should one, some, or all of them run in 2020.
Republicans, meanwhile, have had some success with multiple-time candidates: just focusing on some more recent presidencies: Nixon in 1968 (after 1960). Reagan in 1980 (after both 1968 and especially 1976). GHW Bush in 1988 (after 1980).