So, have you tried with tv fully booted up then the roku?
I have a Harmony remote and have the boot order and delays set. I get a on/off quick switch before everything is settled.
Does your HTPC have a time set where the display will turn off? Say 10 minutes of idle?
Turn that setting off so the display is never turned off. It may help.
Trying the roku on another tv via hdmi may also rule out some culprits.