Even if you are connecting to the Slingbox with Component cabling, you will still see this issue if you have any HDMI cabling running out of the DirecTV box (even if this is just going to your TV). The easiest method to work around this would be to remove the HDMI Cable from your DirecTV box and run another set of Component cabling out of the Slingbox and into your TV. You will not lose any video quality by doing this.
If you still want to run the HDMI cabling from the DirecTV box, you can also consider purchasing an HDMI Adapter. We have an example of one listed on our Accessories Page. I'll link it below, as well as an article that goes over it's use, just in case:
I hope this helps!
Sling Media Technical Support