Well, I don't have a solution yet, but I've learned a bit about how to detect memory leaks. I've verified that I do indeed have one. Here are some quick steps for detecting leaks in your Android app:
1) Install the Eclipse Memory Analyzer. You can do this from the "Install New Software..." option in Eclipse.
2) Set up your application in Debug mode.
3) Download your application to your device or emulator.
4) From the DDMS perspective, highlight your app.
5) Click on the "Dump HPROF File" button.
6) After the HPROF viewer comes up, select the Histogram button.
7) In the regex field, enter part of the name of your app to filter things out.
From there you can see how many objects are available. In my case, I have a class that is called Panel. There should be only one instance of this panel present. After performing several orientation changes (landscape <--> portrait), the number of panels ratchets up... once for each change.
So, now it's a matter of figuring out why. What I've done so far is to strip all graphics and graphics threads out of my app. The problem still occurs. Need to spend some more time on this to figure what's not being released and causing this issue. We'll see where this leads....