I've figured out what was causing the problem.
I have the Onavo Extend service installed, which compresses downloaded cellular data to reduce data plan usage. I understand this is achieved by routing downstream data to Onavo's servers, which compress that data and sends the result via a VPN connection to the iPhone. It works very transparently, so I tend to forget it is there. On a hunch, I disabled its VPN connection in the iPhone settings and retried my failed in-app purchases (after my previous report, I had the same problem in Car Finder), and the purchases executed just fine.
First of all, I've only had my iPhone 5 (my first smart phone) since late November, so I'm no expert.
Having said that, first, be sure you also turn off the On Demand option for the VPN. When I was working on this, I found that just turning off the VPN in the main iPhone Settings wasn't sufficient because it would turn itself back on (in fact, at this moment, every time I turn off the VPN, it turns itself right back on without letting me even get to the On Demand setting).
But after I had resolve my problem, I receive a response from Onavo (firstname.lastname@example.org) giving their recommended workaround for failing in-app purchases caused by their VPN. Here are their steps to follow within the Onavo Extend app:
"Go to the app settings (top right)
Set 'Service Status' to Off
Try using the app."