Hi Clare,
Thanks for responding with your suggestions for solutions. For the record: I'm using 8.1, I can't pinpoint exactly when these problems started, it did happen randomly, and the entire Type Cover would cease functioning.
I'm happy to report that, for a whole evening now, the keyboard has not lost a connection. I think it might be fixed.
Even though I had already done it before, it turns out that Solution 5 (the two-button shutdown) was part of the solution. I had to run it twice and all hardware besides the type cover was disconnected and I was running on battery power when I tried to run the update on the firmware (including my microSD card). For some reason, on my second attempt during that odd setup, it installed the firmware update and I'm now at v2.84.350.0 (for 5/9/2014).
It seems it was the firmware after all, so I hope others are able to fix this. I don't know why the firmware update had so many problems being applied, but I hope future ones are a bit less problematic.
Thanks for the help.