What does an applicant for admissions in a PhD program do if a recommender put down on an already-submitted application suddenly goes AWOL and does not submit his letter of recommendation? Would a missing letter of recommendation completely disqualify the applicant, or does the admissions committee try to make contact with the AWOL recommender?
Although I have not served on an admissions committee, I have been in your situation. There are two things you need to do, both right away. Find a new reference letter writer. When you write to them, apologize for the late notice, but explain that another letter writer is going to be unable to submit the letter(s) they agreed to. In this request, be calm, grateful, and respectful to both the recipient and the original letter writer. Also, contact the admissions office and tell them you would like to change a recommendation writer. I do not think there is need for any detail here. As long as they have letters before the deadline, the administrator responsible for compiling files will add the appropriate letter to your file. The people on the admissions committee may not even know anything changed. Even if they do, I do not think they will care much. They will pay attention to the actual substance of the submitted letters.
Hopefully my story is helpful. A former supervisor submitted about 80% of the letters I had requested from him for my graduate school applications. At first he was simply AWOL. Then I asked a former co-worker to knock on the supervisor's door. The supervisor shouted, "I've had enough with these damn reference letters!" He never emailed me to tell me he had decided to stop writing! I followed the procedure I describe above. The admissions administrators were helpful. I do not believe it had any adverse effect on my consideration in the admission process.