I have a similar issue - latest version of OpenELEC on Raspberry Pi (although in my case this seems to be during playback rather than idle).
I have 4 RPis, but it only happens on the one connected to the TV in my bedroom. So far, I have swapped the PSU, the RPi board, the SD card, the Flirc itself, and done a full reinstall of the software. Still happens on whatever hardware setup is connected to this TV, and I can't reproduce it on any of my other RPis.
Logs on the RPi show it disconnecting after a period of time then reconnecting as 'bootldr'.
I have opened a support ticket - will report any updates here.
Nobuddy0816's comment about energy saving is an interesting one - not sure where this lives on OpenELEC but will investigate.