The phrase on the rocks was originally used for ships which ran aground on rocks and broke apart. Since the late 1800s it has been used figuratively for other disasters or problems. This idiom means,
> Likely to fail because of serious problems
> In a state of difficulty, destruction or ruin
> In a relationship having problems and likely to end soon
> In a relationship on the brink of failing
Also, it is slang term for a drink with ice. A drink ordered on the rocks simply means a alcoholic beverage (usually 2 oz), served over ice.
Example
Their decade long marriage was on the rocks because of one act of indiscretion by him.
The future of the company was on the rocks when the new management took over charge