Of course, you can take them down and then put them back up after your next conversion is over.
But maybe you don't have to. As I mentioned previously, I'm unusually attached to my mezuzot. It was important to me that I could continue to leave them up. So I asked, and I made sure to tell the rabbi that this was important to me. And I was told that I could leave mine up.
I don't suggest asking your congregational rabbi. Ask your beit din rabbi. If you don't have a beit din, wait and ask when you do. (Of course, opinions may differ here.) Congregational rabbis overwhelmingly don't know how halacha applies to conversion candidates and doubtful Jews. The beit din deals with these questions all the time, and they have come to an halachic ruling on the matter. Your community rabbi may have never heard the question before, and if he gives an immediate answer, then you know he has not checked the sources or called a more knowledgeable rabbi. It is unlikely that he knows the answer off the top of his head, and some rabbis, for good or for bad, just want to give an easy answer and move on. He may even believe it is an honest ruling. "Of course non-Jews can't do X!" is not always the right answer. The answer is almost always more complicated, even if it comes to the same conclusion.
The lesson of the story? Ask and you might just receive. But know who to ask and how to ask.