 But if they want to switch back to traditional Medicare, they'll likely also need a Medigap policy. People in those circumstances might find themselves in a bind if they can't purchase a Medigap policy. And often they find out too late. That's because after the first six months of being on Medicare, it can be very difficult to get a Medigap policy. People can be denied a policy because they have a pre-existing condition or they can be charged more.