Open enrollment for Medigap starts the month you turn 65 years old and lasts for a total of 6 months. This is the best time to buy a Medigap plan. If you buy a plan during this period, an insurance company cannot require a medical evaluation to offer coverage, and you cannot be denied coverage based on a preexisting condition., Open enrollment is a one-time period and does not repeat each year like other Medicare open enrollment periods.