Perform Recurring Billing on the 3rd and the 17th of the Month
A business based on recurring payments is usually a good business to be in: the mathematics of the thing are fairly simple, in that you are trying to keep a customer present, happy, and paying for long enough to make more than the combined cost of acquiring and then serving them. For many online businesses, the acquisition cost is the expensive part and the rest is a marginal expense per customer - or at least that seems to be the trend in these days of customer service done the Google way.
In any case, the point is that a simple spreadsheet can show how well your business is doing, what needs to be adjusted, and produce projections for the future. You are trying to reduce the costs of acquisition and serving customers well while increasing customer longevity - the latter meaning a reduction in the dreaded "churn" or loss of paying customers that can occur for any one of dozens of reasons. They get bored, they have a bad experience with the service, they get snaffled by the competition, they unsubscribe to save money, the billing fails, and so forth.
If the monthly cost of your service is in the $5-50 range, then the odds are good that you'll have a bunch of marginal customers. This is more true for some types of service than others, but there will be some fraction of your customers living on the edge of their finances, with cards that frequently fail or bank accounts that are frequently empty. So they tend to fail out of the service in the billing cycle.
The way in which most subscription services manage failed payments is to attempt to rebill the failed payment after some period of time, assuming the customer does not indicate in the meanwhile that they wish to discontinue the service. There are any number of ways to handle how this interacts with whether or not the customer still has access to the service, whether the payment cycle changes, how the customer is informed, and so forth - that is where the complexity lies. Some options are more ethical than others; you can judge the character of a company's founders by how they approach this issue. At the core, however, the mechanics of this are quite simple: pick a time to try billing the customer again, and see if you have better luck.
In the course of my work I've been involved with a number of companies in the US that run low-cost subscription-based services of this sort, with payments largely through credit card processors or PayPal. In each case, the data they gathered quite clearly indicated that some days of the month are far more successful than others when it comes to both ongoing billing of a customer and rebilling a customer after a failed attempt. Your best chances are on the 3rd and 17th of the month, your worst the 10th and 24th - the graph looks very much like a double-backed curve.
The reasons for this are quite simple: most people get paid either on the 1st of the month or on the 1st and the 15th of the month, probably by direct deposit to a bank account. Many recurring billing charges either run from a checking account or via a debit card that draws on a checking account. The best time to bill a marginal customer is after he has been paid, after the transfer of funds to his bank account has cleared, but before he gets to using that money to pay other bills and services. In the US, using the established methods, this turns out to be about two days after the payment date. It is not unusual to see half the billing failure rate in some customer segments if you bill on the 3rd versus one of the worse days like the 10th or 24th.
It will be interesting to see whether rebilling data turns out to differ meaningfully for the brace of younger payment services that are emerging to compete with the credit card and ACH establishments.