It depends on the plan you are on. The monthly plans (Single Basic, Team Starter, and Team Plus) run a month at a time, so you renew each month to carry on. The three-month plans (Single Pro and Team Premium) cover you for a full quarter, so you only deal with payment every three months.
Since nothing is charged automatically, renewing is always your choice. When a plan is near its end, you renew it the same way you paid the first time. And if you do nothing, a paid listing simply drops back to a free listing rather than disappearing, so your business is never taken down for missing a payment.