The ats they let me take home for a few days prior to buying had the same issue with my galaxy note 2. The ats I bought has no issues staying paired. You may want to make sure your car has all current cue updates.
I had this problem initially with my Samsung Galaxy S II. The phone would pair initially and work the first time, but would not connect when I shut down and returned to the car later. I deleted the phone from the car twice and also deleted the CUE pair from the phone, and repeated the pairing procedure but it did the same thing. My salesman, who was pretty savvy about the CUE, told me that there is a dialogue screen on the phone when you are initially pairing that asks a question about automatic connection in the future or a similar question, which you have to okay. I did not notice such a dialogue box. In any event, just as I went out to the car armed with this knowledge and was going to delete and re-pair the Galaxy for the third time, it started connecting, downloaded my phone book, and has worked perfectly since! So I am not sure what I did right, but at minimum I recommend deleting and re-pairing,and monitoring the dialogue questions on the Samsung carefully.