Senator John Tower was rejected by Senate when nominated for Secretary of Defense in 1989.
But it is rare, that is the only case I can recall. The smear campaign was very strong there. I don’t know if his “problems” were as strong as the Democrats painted but they went all-out against him.
[Wiki]: “In 1989, Tower was President George H. W. Bush’s choice to become Secretary of Defense. But in a stunning move — particularly given that Tower was himself a former Senate colleague — the United States Senate rejected his nomination. The largest factors were concern about possible conflicts of interest and Tower’s personal life, in particular allegations of alcohol abuse and womanizing[13][14] The Senate vote was 47–53,[15] and it marked the first time that the Senate had rejected a Cabinet nominee of a newly elected president.”
Ted Kennedy, IOW.
Absolutely right! I remember that case...but, as you say, it’s rare.