Just to recap: when I plug my ac power cord into the laptop when the battery runs low (or I receive a low/critical power warning), I get a critical battery status message and, after a few seconds, my laptop suspends.
Despite spending several hours trying to find a solution, it seems that there are multiple causes of this phenomenon and none seem to fit the the profile of my power issue. During my research, I did come across a cryptic thread in the Ubuntu Forums asking for guidance on how to prevent the power manager from taking any action when the battery level reaches critical. The Power Management editor (System > Preferences > Power Management) doesn't give a nothing option by default in the when battery power is critically low drop-down box, but alesserfate (the OP in the Ubuntu Forums) found a way to encourage Ubuntu to add the option! This prompted me to think that this might offer a workaround, if not a solution, to my problem: I reasoned that, if my laptop takes no action when the power cord is plugged in (regardless of the reported battery state), then I can at least continue what I'm doing uninterrupted.
Using the Configuration Editor (Applications > System Tools), navigate to /apps/gnome-power-manager-actions and click in the critical_battery value dialog.
Simply type nothing as the value and close the editor. If you don't have the Configuration Editor in the Applications menu, you can add it by right-clicking the menu and editing or, open a terminal and type:
Last night and again this afternoon, I've tested the theory!
When the status indicator dropped below 30%, I plugged in the power cord and received the anticipated warning.
However, the warning disappears after a few seconds and the Power Manager takes no further action. The battery continues to charge as it should.
Of course, there is a (potential) downside to this workaround: you can't leave your laptop unattended if there is a chance that your battery will completely discharge! However, it does demonstrate just how configurable Ubuntu can be.