Breaking spokes on adult tricycle
Here is my 2c from over 10 years experience in a busy shop:

I am assuming that it is the spokes are breaking at the hub.
On a drive side wheel, that is where they always break.

There is a different rare condition, when the spoke nipples are breaking off at the rim.
Rims have two sets of holes, one set on the each side.
The spokes might be laced to the opposite side of the rim.
I have never seen this from any bike factory, but rather from amateur wheel builders.   

When a wheel starts breaking spokes, the spokes are almost always to blame.
Aged galvanized spokes that are gray or rusty can have all kinds of microscopic corrosion fractures at the bend.  If the spokes are not corroded, or were made of stainless steel, it could even just be a bad batch of spokes.

Even if a bad wheel build was the original cause, the remaining spokes are damaged and will break with continued use.  Re-tensioning the old damaged spokes won't help.

I am surprised the bike shop replaced the spokes one at a time after the second time it came back.  If the wheel is breaking spokes, it will continue breaking spokes until the entire set of spokes is replaced.

There is one other possibility with three wheelers.
I have not seen a Schwinn three wheeler up close for 15 years or so, but in the old days they had chromed steel hubs, and those can sometimes be a problem.

If the steel hub has a sharp edge in the spoke hole, that is a stress riser.
The spokes break right where the spoke bend hits the sharp corner.  Aluminum hubs are softer and will deform a bit - no sharp edge, no stress riser, no breakage.  

The drive wheel on a three wheeler uses a special hub, special made for that exact trike, so you are pretty much stuck with the hub it came with.

I have lightly chamfered the spoke holes in some problem steel hubs with a countersink bit to remove that sharp edge.  A dab of paint to avoid rust is useful too.  

While the chamfering makes logical sense, and those wheels never came back, it is hard to tell if the chamfering did the trick, or if a set of new high quality stainless spokes was enough to cure the problem.

If the trike is only a year old, it should be a warranty repair to get a proper fix, not just one spoke at a time.  Either replace all the spokes with quality stainless spokes, or replace the wheel.  I would trust a new set of spokes more than a replacement wheel.  If the shop won't handle this under warranty for a one year old trike, then contact the shop owner, or go up to Schwinn corporate if you need to.

Hope this helps.