Disagreement with client on project termination

Hello, I am a freelancer who had been engaged to develop an app for a client. It was a one month project ending 6th Sep. I had informed the client that I might get other assignments in September and am free only for the period of the project. The client had paid half of the total project amount at the beginning of the project. But due to delays in inputs from the client's end, development was stalled for a significant amount of time and the project overshot the target delivery date. I informed the client in the middle of September that I would take around 3 more weeks to complete the project. Hearing this, the client wanted to close the project and is asking for the advance back. I have put in a lot of effort on this project and don't want to return the amount, since it will result in heavy losses for me. What options do I have and how should I proceed? Thanks.