Sure, there will continue to be trade, but the need/desire to trade will be reduced.
To look at how/why, you need to look at decentralised production. Technologies like 3D printers promise to be able to produce many of the products we currently trade for, and this goes beyond the plastic trinkets people currently associate with 3D printers (there are already 3D printer devices in the fields of clothing, food, medicine, heavy machinery, etc...). So whilst there will be trade for the raw materials, why would you pay someone else to make something for you when you have access to a machine to do it for you (note that I said access, not ownership, I don't expect everyone will own a device that can create a car, for example)? It makes sense for people to cut out the middle man when the end result is just as good as they could've gotten by paying a premium.
There will still be people wishing to trade for things they can't get for low cost locally, but there will be a lot of industries disrupted by the ability of people to produce their own consumer goods.
I've heard it said that, "even God hesitates to offer anything but bread to the starving man."
People like to trade stuff. This means there will always be things people want to trade. This means money, commerce, and scarcity aren't going anywhere.
The post-scarcity folks seem to assume that there is some basic set of things: food, shelter, healthcare ... that once we have, we'll be "done"
It's never going to work that way.
Let me put this another way. We live in a world with millions, perhaps tens of millions of millionaires. Folks that if they wanted would never have to work again.
Do these people stop working? Do they stop accumulating and trading things? Is their participation in the economy so drastically different than others?
The poorest person in the U.S. is living a better life than the richest person alive 1,000 years ago. Do they live in any fashion similar to those folks? Would those folks, if they could see 1,000 years into the future, guess at how the common many would behave, given all the things he has?
Post scarcity is a nice sentiment, it just doesn't work.