A business operating online can continue to operate on Shabbat. This is stated by Rabbi Shmuel Polchak in an article published in Tchumin LD, the recently published halachic yearbook of the Tzomet Institute.
According to the article, reported on Channel 7, businesses operating online can also be operated on Shabbat, according to the "Contracting in Large Businesses" rule, since in today's reality, if a solution is not found for operating a business online on Shabbat, it will lose large audiences, because "the users' expectation is that these services will operate without interruption, and will even provide customer service at any moment.".
Rabbi Polchak states that it is possible to enter into a contracting agreement with a non-Jew, or with a company owned and managed by a non-Jew, to operate the business on Shabbat.
According to him, in such circumstances, it should be permitted to rely on the "Contracting in Large Businesses" permit, which deals with such cases, and hire a non-Jewish contractor who will manage what is required to run the business on Shabbat and will be paid according to his output.
Rabbi Polchak, a researcher from the Land Law Institute in Ofra, notes that if it is possible for a Jew not to explicitly tell a Gentile contractor to do work on Shabbat - that is preferable, but if it is necessary to define for the contractor his tasks for Shabbat - it is permissible to explicitly tell him Shabbat eve, and not just by implication.