They sit and wait until their money for the observing trip runs out, then they pack their bags and return home. You can't mess with mother nature, and it is common for about half of your observing time to fall under the rubric of 'non-optimal' for a given research program you are trying to conduct. This is more common at optical and infrared wavelengths. But even at radio wavelengths, you do not want your million-dollar receiver sitting out in the rain, even though it can see through virtually all forms of bad weather. If you need a certain kind of data that you can only get by direct observation, you really are stuck. All you can do is wait it out and try again when the weather gets better. There are no shortcuts.