What you are describing is almost certainly IR inteference from the backlight on the TV. As the TV warms up, the problem goes away.
Solution:
Best solution. Go to RF on the remote/receiver. If you don;t have an RF-capable remote, you can buy one from people like Solid Signal, or from DirecTV.
Other solutions.
Move the DirecTv box to a slightly different location. Turn down the backlight control. Put a piece of blue tape over the IR sensor on the DirecTv box (yes, it works!)