As for a solution, not sure. The only references I have found to people solving the problem all involved talking to the router manufacturer. You can't do this by changing anything on the DirecTv boxes, they are working as they are supposed to be.
Some suggestions:
Make sure you only have one path to the internet from your DirecTv boxes. . Sometimes people set up wired and wireless, but if you only have the Genie and clients it can't be that..
get rid of all mac blocking. It's a waste of time anyway, any hacker can soon find out which mac addresses work and then spoof them.