I might have my problem figured out. Or at least, this is what's working...
I was using the Flirc XBMC power button to put the Fire to sleep, but it was the one that was unreliable. I've now changed it to Flirc's Computer Media Keys power button, and it seems to be working as expected. Which is actually very good for a device with no power/standby button.
My Samsung TV and my Yamaha amplifier both only have a single power toggle button. A long time ago, I was able to scrounge the Pronto hex codes for them to create discrete on/off buttons in the MX-500 using a vintage Palm TX and an app called NoviiRemote. I figure it's only a matter of time before someone like Jason figures out the discrete codes to make the Fire sleep/wake more properly. As it is, power toggles so I left it out of my system off macro.
I'll be sending the Harmony back. It's pretty, but I didn't really need it. And MyHarmony keeps hanging up during the sync process. Plus I can punch in a macro on the MX-500 faster than it takes to sync the Harmony when it does work.