Something is stealing focus from MC Theatre View shortly after you start the PC, but not immediately, which is why the left and right buttons work when you stay with the PC and test straight away. Steam (the gaming software) will do that for example, but so will lots of other software. Check your Windows Startup items if this is the cause.
If you have a mouse connected to the PC and clicked on the background in Theatre View when the left and right arrows don't work, do they then start to work again? I would expect so.
If you have the equivalent of a MCE Green Button in your App, that should also pull focus back to MC, and the buttons should start working. I use a Harmony remote control which uses the MCE "Media Center" command to replicate the MCE Green Button, for example.
BigSpider's question is very valid though. JRemote, I would assume. Some remote control Apps will work even if MC isn't in focus, at least the Android devices. I no longer use iDevices so can't comment on the Apps run on them.