Including Truman in this as a two termer makes this just silly.
Really doesn't point to anything at all. I have a 4 leaf clover.
If you are going to count a dead Presidents successor or one who resigned, then it should be:
Number Name From To Party Years
3 Thomas Jefferson 1801 1809 Democratic-Republican 8
4 James Madison 1809 1817 Democratic-Republican 8
5 James Monroe 1817 1825 Democratic-Republican 8
16/17 Lincoln/A. Johnson 1861 1869 Republican/Democrat
18 U. S. Grant 1869 1877 Republican
32 Franklin D. Roosevelt 1933 1945 Democrat 12
33/34 FDR/H. Truman 1945 1953 Democrat 8
34 Dwight Eisenhower 1953 1961 Republican 8
35/36 JFK LBJ 1961 1969 Democrat 8
37/38 R. Nixon/G. Ford 1969 1977 Republican 8
The last time a twice-elected President was followed by a twice-elected President was when Cleveland was followed by McKinley. Of course Cleveland's two terms were not consecutive, and McKinley was assassinated half a year into his second term, but both men did win twice.