Fishing and Commercial websites
In previous halakhot we explained that the rabbis of the Mishna (200 CE) discussed the status of self activated devices on Shabbat, programmed before Shabbat begins. The rabbis authorized for example, to set fishing nets on a river on Friday,knowing that fish will be caught during Shabbat. The caught fish, obviously, must be removed after Shabbat (See link)
We learn from the case of the fish nets, that a profit generated during Shabbat, if no human action was involved,it does not represent a Shabbat problem. For this reason you can have stocks or money in a savings account, although it will generate a profit on Shabbat.
Can we apply the same logic to a commercial web site, and authorize a Jew to keep his web site 'operating'automatically during Shabbat?
Modern rabbis are divided in the interpretation of the web site case, vis-a-vis the fishing nets of the Mishna. Some rabbis (Shebet Halevy, 10,57) would not authorize a web site because, unlike the case of the fishing nets, there is a principle of 'trade' involved in the website. This is apparently the opinion followed by some companies like www.bhphotovideo.com whose website remains available 24/7/365, but orders are not 'accepted'until Shabbat ends.
It seems, however, that the majority of modern orthodox rabbis authorize to have a commercial website self operating on Shabbat, with 2 conditions
1. That the majority of potential customers are not Jewish customers. This will exclude for example, an Israeli/Hebrew site or a Judaica store website, etc. (See link)
2. The orders are 'processed'after Shabbat. In other words, the whole money charging process (checking credit, charging the credit card) takes place during Shabbat in a completely automatized way but human intervention begins only afterShabbat, with the shipping process.
In these terms, most rabbis, including our own rabbi Ben Hayim, would authorize keeping a commercial web site active during Shabbat.