What makes 3D printing noncompetitive for medium production runs?
TL:DR

3D printing is great for low quantities of items, but terrible for large quantities of items.  This is a continuous scale and as your quantity grows, the drawbacks of 3D printing become more pronounced.  In your situation, you seem to be dancing in the nebulous zone where there isn't really a good answer as to which production method is better.  It's more of a question of price vs speed.

There are several factors that limit additive manufacturing technologies (in this answer I'll just talk about FDM since you're asking about a plastic item) from being practical in large scale manufacturing.  

Time

Compared to injection molding, 3D printing takes a very long time.  An injection mold can make 72 plastic caps in 3 seconds.  While I don't have a source, I would expect a similar item to take at least 5 minutes to be printed.  In order to produce an average of 24 caps/second, you would need 7,200 3d printers working without down time.  That doesn't take into consideration ...

Labor

Every 3d printed object needs to be removed from the print bed by hand.  That requires a person to be there ready to remove the item.  It's possible to have automated print removal, but for now I've yet to see it as a standard option on any machine.  An injection model machine can just pop the parts out into a box.  Even with the capability to remove the parts extra labor is still required for 3d printing because ...

Quality

Injection molded parts are as smooth as the mold they were made in.  While failures still exist even for molded items, their relatively cheap production cost and very quick production time ensure that an occasional failure won't be problematic.  3D printing on the other hand is still prone to variations in the final product.  For a few items, it's sensible to hand finish the parts with filing, sanding, or other reductive manufacturing techniques, but for many items this quickly become burdensome. Also, given the long production time compared to injection molding, even 1 discarded product will result in a long time required to produce a replacement.