I have some additional information about this situation. As I thought, IE was timing out before the credit-card issuer was able to respond with a confirmation. The same thing has happened several times since then, including once as I was attempting to purchase tickets for a flight to South America. I prefer to use IE for such things because Adobe Acrobat has added a "Convert" toolbar button to IE9 so that I can get a PDF file as proof of payment (with Vista or Win7 you can no longer use the "print to PDF" option due to security issues). As far as I can determine, the convert button isn't offered with any other browser. Eventually I found a setting in the registry that affects the amount of time IE9 allows for responses. Here is the registry key:
HKEY_CurrentUser\Software\Microsoft\Windows\CurrentVersion\Internet Settings
The value that controls the setting of interest is a REG_DWORD named "ReceiveTimeout". The default setting is 10000 ms, or 10 seconds. That's too short for most credit-card processing. By changing it to 120000 (equivalent to two minutes) I was able to overcome the problem. It's odd that Microsoft set this value so low, and even odder that you can only change it through the registry. I suspect that it will cause a lot of people to stop trying to use IE9 for online purchases.