Issue is probably to do with HDMI connection recognition, so it seems that yes you are on the right track in trouble shooting.
If you can try another HDMI cable or another thing to try is an HDMI switch. That Switch can cost a few dollars thou and may not fix the issue. So try another cable first and with a powered off Buzz box when connecting or disconnecting. Even try with the Buzz powered up if else fails.
I did have the same sort of issues here with this Buzz xpl and tried a few HDMI cables but in the end the Switch got it working and now I no longer need that Switch and will work with previously failed HDMI cables.
I did already have a Switch, so it was handy.
An HDMI Switch is basically just a hub with extra HDMI slots.
These HDMI connections can carry a variety of signals, including... power, internet, audio/Video... so they can fail or even partially fail and even work normally after again.
Could also be the TV refusing to recognize the HDMI connection ....after that sleep it had