Grace periods are a way to keep your products active for one (1) extra day, despite missing your due date. This one (1) day would start with your due date being day one. Meaning that if your service were due on the 1st, you would be able to keep it active until the 2nd.
Grace periods are automatically issued when a payment is missed for services that would qualify.
Domains and any service Billed Hourly, would not qualify for a grace period.
What if My Product is Suspended for Lack of Payment?
Currently, the only way you could be suspended for lack of payment is if you had gone past the one (1) day allotted in the grace period. If that has happened, the only way to reactivate your service would be to pay for it.
Grace periods do not change your recurring due date or have any effect on any Automatic Payments that you may have in place.