What do I do if I run out of things to say during my oral exam?

Most importantly, I would stress the importance of not panicking! It is completely feasible that you could exhaust all the resources of one line of conversation, as is possible in every-day parlance. However, just because you might exhaust your own resources, doesn't mean you've used up all the examiner's knowledge. By asking questions such as "¿está de acuerdo con lo que he dicho?", you're able to show engagement with the examiner, a mastery of different tenses, as well as eliminate a lengthy silence. This can then provide other material for you to use to spark further discussion.The previously mentioned question in particular further brings up the topic of register. Within Spanish, there is the formal "Usted" form, and the informal "Tú" form. The main take away point here is to establish your game plan before the exam. If you are going to address the examiner formally, you have to consistently utilize this style throughout the conversation. Successfully executed, a consistent style will stand you in good stead to not drop marks grammatically, while preventing confusion during the exam.