My HDMI died as well (I got 6 weeks out of it). Unfortunatly, repeated calls to Dish, they simply refuse to replace it, blaming software. I cancelled service (component audio has always been out of sync, they know of this problem too, not even a hint of an ETA on that fix), and took the cover off. Thermal cycling is a high probability cause. The surface mounted connector on a plastic board is secured with a screw to the metal backing. Everyone except the receiver designer seems to know that metal and plastic don't expand equaly.
Anyway, suppose your HDMI is working right now and you have no plans to move it whatsoever. If you were to fully secure and support the weight of the cable so that there is no support required by the receiver, you might want to loosen the HDMI connector screw a couple of turns. If the screw is not locked to the metal back (thereby stressing the surface mount points) when the PCB expands, there will be no induced stress on the HDMI connector, it won't eventually break the solder joints and you should be HDMI toruble free forever. Just remember, do not move anything, especially the cable, until you retighten the screw. Preferably when it has completely cooled down. Take a look at your box, you will see how seriously bad the design is.
Here's a couple of pictures of the problem.
http://mostly-linux.blogspot.com/2006/09/dont-blindly-believe-dish-if-hdmi.html
TripleII
Aside: 7 weeks of runaround, even telling them of all I read about here, and they still refused to replace the box. After looking at it, I called, they said they can now send a new box, I am important to them, but alas, it is too late, I am done with Dish. How many of us would have understood, and accepted the problem until a real solution was found if Dish just came out with the truth. Also, how many people are out there, don't know it isn't their TV, swapping cables, purchasing component cables, hastling their TV manufacturers, and on and on. Way to go Dish.