An app charges users by subscription. It runs by itself. People sign up on Shabbat, subscriptions renew on Shabbat, a payment processor charges the cards, and no person touches anything. Both owners are Jewish.
I saw the answer here about owning shares in a company that operates on Shabbat, that a shareholder is not really an owner. This is different. It is a small private company and he is one of two owners.
1. Is money that comes in on Shabbat sechar Shabbat? Is a monthly renewal that happens to land on Shabbat different from a one time purchase made on Shabbat?
2. Servers run and a processor charges a card, and no person does anything. Is that anything at all, or is it counted as his because he set it up before Shabbat? A Jew’s tools are not commanded to rest the way his animal is.
3. The processor and the hosting company are companies, not a person he asked to work for him. Is there amira l’akum here, or is a company just a machine with paperwork?
4. Maaseh Shabbat. If the app produces something for a user on Shabbat, may he keep that money, and may a Jewish customer use what he got?
5. Both owners are Jewish. Is the only real fix bringing in a non Jewish partner, or is there something a company with only Jewish owners can do that actually works for software? And is giving the Shabbat income to tzedakah a real answer or a fiction?
6. Marit ayin, and what a person should actually do. Shut off signups for twenty five hours, or let it run.
I think this is much simpler than the question makes it sound. There is nothing wrong with a Jewish-owned app, website, server, or payment system continuing to operate automatically on Shabbat. The Shulchan Aruch permits starting a process before Shabbat and allowing it to continue on its own, because אין אדם מצווה על שביתת כליו … our machines do not have to keep Shabbat (O.C. 252). Buying and selling on Shabbat is a rabbinic prohibition on people conducting business, גזירה שמא יכתוב (Rambam, Hilchot Shabbat 23:12). Here nobody is conducting anything on Shabbat. The computer automatically processes a signup, renewal, payment, or download because the system was set up beforehand.
Therefore, I don’t see amira l’akum, maaseh Shabbat, sechar Shabbat, or a need for a non-Jewish partner. A monthly subscription is certainly not sechar Shabbat merely because its automatic renewal date falls on Saturday, and there is no reason to give the proceeds to tzedakah. A Jewish customer who personally goes online and makes a purchase on Shabbat may have his own Shabbat issues, but that does not make the Jewish owner responsible for what the customer’s computer is doing. Practically, leave the app running. We keep Shabbat; our machines don’t.