Question

What happens when a hypothesis is not supported

Answer 1

 For a start, when you have a question that needs answering in science, you formulate a null hypothesis. That is a negative statement which you then set out to prove or disprove. This is just a convention. So if your initial question is for example, "Does sugar dissolve in water?"

Your null hypothesis will be "Sugar does not dissolve in water."
You then set up your experiment and get some data.

Now if your data doesn't support your null hypothesis then you reject it and make the statement ,"Sugar does dissolve in water." As you can see from this simple example, a non-result is still a result so the idea of formulating new tests as mentioned by another answerer isn't necessary and in some ways is the incorrect thing to do. In science, hypotheses are often not supported by data and i would argue that this is the case a lot of the time. A non-result is still a result and you will have plenty to write about whichever way it goes.