Hey there pknyzf,
That is strange indeed! I'd be happy to help you look into this issue a bit further. What I am thinking is this may be an HDMI-CEC issue if the remote works just fine with the TV on, but not off. Double-check that your TV doesn't have any power-saving settings on that may affect the CEC while the TV is off. It may also help to try using different HDMI ports on the TV to see if they all act the same.
I hope this helps, let me know if you have any more issues.