How to stay in connection with a professor when you want to apply for the position in his group in next quarter?
You could contact him to ask for him to advise you on some papers for you to read that are related to the work for that position. This way you have a good excuse to contact him, you gain extra points for showing interest and getting prepared in advance, and also provides you with another excuse to contact him in the future to clarify questions you may have from reading those papers.