I have tried to connect both the HDMI and the component out of my HR 21 at the same time. I am not trying to use both feeds at the same time. This works until I turn off the HR 21. It will not turn back on without doing a total reset and disconnecting one of the connections. Is there a work around for this?

Don't turn it off. Only the front panel lights and outputs are affected. All the internal workings remain on. Turning off the HDMI output is probably interfering with the negotiation or handshaking between the HDMI connections.