Please can you tell me if it is ok to sell via Amazon and keep the listings up over Shabbos?
I am a private seller and do not use Amazon fulfilment. When and item is sold, any money is held by Amazon for a number of days before being transferred automatically to my account
Assuming your business is not processing any orders on Shabbos this would be permitted. The fact that others are placing orders on Shabbos and giving their credit card information poses no problem for you.
See Noda Biyhuda (Tinyana, Orach Chaim 26), who writes that there is certainly no problem for somebody to receive money for a sale that is performed on Shabbos.
When the sale is permitted (see Orach Chaim 323:4 concerning purchases for the purpose of Shabbos, and Orach Chaim 245:5 concerning a non-Jew who sells on behalf of a Jew), there is no prohibition of “making money” on Shabbos. Just as it is permitted, in this instance, to “make money,” it is likewise permitted for the sale to be completed.
A similar idea is found in Shut Beis Shlomo (Orach Chaim 36) and in the Tehilla Le-David (244:11).
Based on this principle, authorities have permitted the placement of vending machines (selling drinks or other commodities), even when they will be used on Shabbos (in areas where the use on Shabbos will be by non-Jews; see Shut Maharshag 2:117; Shemiras Shabbos Kehilchasa, in the name of Rav Shlomo Zalman Auerbach, Chap. 29, note 71). The same would apply to your sale on Amazon.