It is well known that you will have to appear for interviews if you had filed applications for US citizenship, Green Card or for adjustment of status. USCIS will adjudicate your case only after the required interview. USCIS allows the applicants to reschedule their interviews but the USCIS requires the applicants to provide valid reasons to reschedule the interview. You will have to provide a good reason why you are unable to appear for the scheduled interview and why you need to reschedule your interview.
US immigration laws state that your application may be denied, if you do not appear for the scheduled interview. In that case, USCIS officers will consider that you had abandoned your application. If you do not provide a valid reason, your application may be denied and you may be required to start the process again and you will have to file a new application and pay the filing fee again. If the USCIS officer denies your US citizenship or Green Card application, based on abandonment, you may not be able to appeal but you have an option to file a motion to reopen the case or you will have to file a new application.
However, the USCIS officer will decide whether to reschedule your interview or not and it depends on the reason why you are unable to appear for the actual interview. You will have to prove that you cannot appear for the interview at the scheduled time because of a medical or family emergency. To reschedule your interview, you will have to go directly to a USCIS office and speak to an immigration officer and explain your difficulty. If not, you may send a letter to the immigration officer, if you feel that you may not be able to appear for the interview. Remember that you will have to show that you cannot make it for the interview for reasons beyond your control. If you are not prepared for the interview and if you say that you are not ready for the interview, the immigration officer may not accept your request to reschedule your interview.
If the immigration officer considers your reason, your interview may be rescheduled and you will receive a new interview notice. However, you must not skip the interview date and if you do so, your US citizenship or Green Card application will be denied. It is wise to appear for the actual interview and if your situation does not permit you to appear for the interview, you may reschedule it. But the USCIS will accept your request only if the reason is strong enough. If your request is considered you will receive a new interview notice from the USCIS. You will have to start over again, if the USCIS does not accept your request.