Many employers completely prohibit relationships between management and subordinates.  The military has some complicated rules regulating relationships and it too prohibits relationships between those with very different ranks.  But, studies show, nevertheless, that relationships continue in the workplace.  The workplace remains a prime source of marriage partners.  But, the problems developing in the wake of David Letterman’s revelation about his relationships at CBS show the danger involved.  Even after ending the relationship, they can fester and develop into sexual harassment.  Co-workers can take sides in some perceived conflict and start a hostile work environment.  

Such relationships can become sexual discrimination if the employer takes adverse personnel action against one party but not both.  There are many traps for the uneducated.  That is why most large employers simply prohibit them.  CBS prohibits them, as this story explains.  So, yes, it is fair to say that Mr. Letterman could lose his job over this.  If CBS punishes no one, then it risks that no one will take its policies seriously.  If they punish the female subordinates but not the male manager, then it looks like gender based discrimination.  Looks like a no win situation for CBS, at this point.