I fixed the problem.
The problem was that subforms below the instance I was adding were positioned, so the new instance went UNDERNEATH them and were hidden.
I found that when making a dynamic form, it's best to wrap all objects in positioned subforms, whether or not you plan on repeating them, and then wrap the positioned subform in a flowed subform by itself. Finally, make the page-level subform a flowed subform. A flow-direction of Western Text works best.
You might be able to do without some positioned subforms and just wrap everything in flowed subforms, western text, but LiveCycle will left-justify everything unless you put spacer objects like empty text boxes on the form to keep other objects in place.