Right now, if we put the renewal date on the 1st of each month, it seems like a customer who subscribe just the day before will have to pay for 1 day then need to pay again the next day to renew their subscription. Most system that allows this option will give you the option to say a minimum of days to the bill, so if it's below that number of day, it will bill the current month + the upcoming month.
Example
Number of days in the month: 30
Monthly Price: $60
Renawal day: 1st of each month
Minimum days to bill: 10
Subscription day: 28th
In this case, it would bill the customer $64 (2 days in the current month + the upcoming month)
Subscription day: 19th
In this case it would bill the customer $22 (11 days in the current month)
So it avoid creating invoice that the amount is so low that the payment gateway get a big chunk of the amount in fees (or in some case, all the amount).