Do graphs work in Custom Components?

I built a custom component (first time I've tried this) containing two Axes objects as well as some text fields. Here's a picture. I've been having some problems.

1. These graphs appear one size in the editor, and larger when an instance of my component is inserted into my app. (Compare the relative size of the graph to the text fields, in the picture above in the picture below.)

2. Some fraction of the time, when I run the app, the Axes objects don't appear at all, although the other parts of the custom component do.

Is this a known bug? Is this usage of Axes objects a hopeless mess? Or is there some way I can tweak it to get around this problem.

Component embedded in app:

App running: