"It is not unknowen unto you, how they stroke upon these rocks."
John Daus, Sleidanes Commentaries, 1560.
'On the rocks' has been used metaphorically for centuries to refer to disaster and ruin. This is in analogy to a boat that has run aground; this is not necessarily the end of the ship, but it is certainly not good. It is has slightly different meanings depending on context.
1. When referring to an individual person, "he's on the rocks", it will most often mean that he is having severe financial troubles, but can refer to other sorts of trouble, such as a mental breakdown. It most often suggests that the person is broke, but could also be used of someone who is facing bankruptcy.
2. When referring to a company, it will nearly always refer to financial troubles, such as pending bankruptcy.
3. When referring to negotiations, it means that the parties are not able to reach a deal, and things are about to fall apart.
4. When referring to a marriage or other romantic relationship, it means that the couple is arguing. It may be used even when a divorce or breakup is not likely, although it would not be used for a small spat or disagreement.
5. In a completely unrelated sense, 'on the rocks' can refer to a drink, most particularly an alcoholic drink, that is served with ice. This usage first appeared in 1946, but other than a possible connection between the various slang terms for diamonds (rocks and ice), it is most likely that this is simply a bit of low wit that will forever go uncredited.