Brand new Subaru Forester, possible electrical issues?

I just bought a 2015 Forester Limited and have put about 1000 miles on it. I love it, and it's the first new car I've owned in a long time, as well as my first Subaru. I regret to say that I've had already had some trouble it, which I hope does not portend future issues. I have had some problems with the power lift gate not opening using the button on the dash- it beeps three times but doesn't open, regardless of the position of the key in the ignition (car is always in park when I attempt it, and the owner's manual indicates that it is supposed to beep twice before it opens). If I first use the key fob to open and then close it, I'm able to get the button to open the gate but I don't have any idea why the gate won't initially respond to the switch on the dash. It's worth noting that this doesn't happen every time I try to open the lift gate using the button, so I've been unable to reproduce the problem for the dealer. Is there a software reset that could fix this, or is it an electrical issue?
The second issue is another intermittent one: the entire heating and cooling system wouldn't turn on after being shut off. I drove a couple hours with the AC on, shut the AC off, parked the car and then restarted it after an hour. When I tried to turn on the AC, I was unable to do so- the entire heating and cooling system was unresponsive. The AC button wasn't responding, I couldn't adjust the fan level, and the mode selector (vent/floor/defroster) wasn't responding either. I pulled over, shut the car off and restarted it and was able to turn on the AC without incident. Any ideas what happened and why, or even what I should be looking for? I wasn't able to reproduce the problem here either.
The car is at the shop as I write, I hope they're able to figure out what the issue is so I can just enjoy my new car.
Comments
the tailgate does sound like a programming issue, given how you describe it, so maybe the dealer can just work that out for you fairly easily
As for the HVAC system being unresponsive, that could be related to the control panel; hopefully that's a problem they CAN reproduce right in the shop.
Thanks, Mr_Shiftright. I brought it to the dealer, who (of course) was unable to reproduce the problem. I had a similar problem again today, when the whole system just quit on me while I was sitting at a stoplight in stop and go traffic. I couldn't get it to turn on, the fan wouldn't run, there was zero response from any of the switches and dials on the AC. I had to restart the car to get it to work again, but even then the AC wasn't cooling effectively. I don't know if it's relevant, but the AC wouldn't cool prior to that, and the car had been parked for almost two hours while I was at the gym. So, it is going back to the dealer again tomorrow, where I suspect they won't be able to figure out the problem. Should I insist that they do something like replace the module governing the AC? I'm getting frustrated with these issues, this is a brand new car and I don't want to hate it for the next several years. Everything should work perfectly, even under taxing conditions, and that's not happening with this car. The AC also doesn't cool some mornings at startup if it's less than 70 degrees out- it just blows lukewarm air. I need to turn the AC all the way down to 60 degrees, wait for it to start blowing cold air, then turn it up to about 65.
Too bad. You might mention to the dealer that you will be exploring your state's Lemon Laws (actually might be a good idea for you to at least get up to speed with this).
The dealer won't replace anything unless he can prove to the factory that the part was defective; otherwise he has to eat the repair himself---naturally he'd be reluctant to do that.