When to remove a Product from Amazon
When you are out of stock in a particular product and are never going to refill your stock then it is appropriate to take the item down from Amazon (and your own web-store).
If you are temporarily out of stock and expect to get more stock back in then it is not appropriate to remove an item from your web-store and from Amazon. The stock level is one of the feeds pushed to your web-store from your POS. Both your web-store and Amazon will not sell if your stock level is less than 1.
How To Remove a Product from Amazon
If an item is removed from your web-store then it will be taken down from Amazon.
If you set up a field mapping in NScPAM that determines whether an item should be pushed to Amazon, map this to a custom text field using NScSync and map include_in_amazon to this field, then all items marked false in PAM will get taken down from Amazon.
Word of Warning
When you take an item off Amazon, Amazon will not let you re-list that item for 24 hours.