When 2nd time my battery dead i didn't use the remote start, but they found something else drain my battery while the car is turn off.A new yukon should last 30 days if it's left alone (locked, no keys in it). if you start it a few times a week for 10min a crack you'll drain the battery. If you are in and out of the vehicle you will also drain the battery.
For you,
Have the battery load tested and don't remote start the vehicle if you aren't going to use it.
Its something in my rear climate control give a signal to battery + they told me to bring my 2nd key because there is some power goes on while the key inside.
I am still waiting for the 3rd week now and my car at the dealer.