The memory jogger for the rule is 'ace, base, grace'. Base month is the month that the renewal/checkride is due. Ace is the month prior ie 1 month early, and grace is a...well, grace month to meet the requirement even though past due. The ace, base, grace rule doesn't change when the next check is due ie 6 or 12 months from the base month.
Just like some loan or overdraft repayments. You may be allowed a bit of leeway to pay slightly late but it doesn't change when the next payment is due.