When testing is delayed, you are at greater risk because the abnormal cell changes are not detected early. If you have had your cervix completely removed, during a hysterectomy for example, and have no history of an abnormal Pap, it may be fine to discontinue the test.
The question of how long you can go without food depends on a lot of factors. Will and determination definitely play a part. Political prisoners on hunger strikes and fasting religious leaders have been known to go for weeks at a time without any food. Gandhi fasted for 21 days while in his 70s. People lost in the wild have also survived for long periods of time without eating. Medically speaking, most doctors agree that healthy humans can go up to eight weeks without food as long as they have water. People have gone longer and been fine, and people have starved to death in less time.
In addition, humans can actually survive crazy amounts of time without any type of food, liquid or otherwise, as long as they still have adequate water. Depending on health and body size, it's estimated that a healthy person can last between 30 and 40 days without eating a single bite. In one extreme case, a 456-pound man lasted an astonishing 382 days without eating any food, solid or liquid, ABC Science reported. Over the course of his year of starvation, the man dropped down to 180 pounds and was able to keep the weight off for five years.