Like the suggestions before it, this is a good one, although harder to implement.
Router is not easily movable.
But I was able to string ethernet cable up two flights of stairs to connect Hopper directly to router.
And I then carried the laptop down those stairs to use patch cable to connect it directly to router.
So, with only cables and no WiFi between Hopper or router or laptop, DishAnywhere.com still thinks Hopper is not connected even though Dish's own connectivity test says everything is fine.
Have posted this problem to Asus support line. (I wonder if there's a router setting that would solve the problem...)
Will contact Dish again to see if this new information changes their view that it's a Hopper software problem.