Automatic Transmission problems of the 2006 Hyundai Tucson

My Hyundai Tucson will stall each time the vehicle is driven steadily at highway speed for 20 miles or so. Getting back on surface streets it begins to suddenly downshift into 2nd or first when slowing or braking. Following this, the vehicle will stall if it gets slow enough or you come to a stop. I fear being rearended or left in a lane to restart with traffic bearing down. The internet has several instances of the same problem with no resolution from Hyundai. I add my information, in hope it will save someone and solve the problem. I have owned the vehicle 4 months and I'm the 3rd owner, bought from Hyundai lot.