Do the chances of not waking up increase with the amount of times a person is put under anesthesia?

Unfortunately anything is possible, but what you're describing would be extraordinarily rare especially if you are healthy. At least in the U.S. elective outpatient surgery is limited to six hour max and is often less. Rare allergic reactions can occur from anesthesia, but  are extraordinarily unlikely. You should absolutely do what you are most comfortable with,there is no such thing as no risk, but interestingly I suspect the risk of driving would exceed the risk of not waking up from an anesthesia.

Anesthesia is very safe.  Having previous surgery safely should not impact further surgeries under anesthesia.

Thank you for your question. Complications with anesthesia depend on your underlying health, the length of the surgery, the risks of the surgery and where you have surgery. A generally healthy person undergoing an hour surgery/procedure associated with minimal risks and a board-certified anesthesiologist will most likely have less complications compared to someone who has multiple medical problems undergoing surgery that has high risks. Typically, your board-certified plastic surgeon will review your medical history and discuss the risks of surgery as they pertain to you. He/She may then send you to have pre-anesthesia testing to help identify your risks for anesthesia. You will also have a chance to discuss the risks and benefits of anesthesia with your anesthesiologist before the procedure. I recommend that you ask questions and make a decision based on your level of comfort and the expertise of your surgeon. Good luck.