It shouldn't interfere with you getting a refill, but as a precaution you should refill in plenty of time, in case the pharmacist has to call your doctor for an okay.
Going a long time without taking a break to let your body have a period is not great for you. Your endometrial lining needs to shed. When you do stop the pills, get ready for anything in regards to the period that comes. It might be normal but it might be heavy, and it might be darker or browner than usual. If you get a lot of cramping, ibuprophen helps a lot.
Talk to your doctor, if you are worried. And also, read the package insert next time! :)