I don't know what exactly are the compounds that causes urine to be smelly, but does it (or do they) have higher or lower boiling points than water? If I have both liquid and exposed them to open air, will the water dry up first or will the smell disappear first?
There are several reasons that a smell vanishes.
One obvious reason is that a smelly component has a very low boiling point and simply evaporates. Another reason might be a chemical reaction of the "stinker" when exposed to air, which converts it to something untraceable.
On the other hand, other reactions might result in quite the opposite but I rather doubt that you want to perform a test run with open bowls of urine over the next week at home ;)
Here is an older article from 1971 on the gaschromatographic analysis of volatile organic compounds in human urine after extraction with diethylether.
On a first view, however, the ketones that they found usually have a rather nice smell.
Again, the ketones usually have a pleasant smell, but they also identified some of the highly volatile bad boys, such as trimethylamine, methanthiol, and dimethylsulfide. These have boiling points of ~5, ~6 and ~40 °C, respectively.