Not sure the age of your Batteries but could be the range on the Remote are lower do to a weak battery in the remote or weak in the car.
In Theory your RS should work if the car is off, doors locked hood closed and you don't have a Check Engine light on or Low fuel and also good battery.
Was the problem something that has happened more then once? What did you do to make sure that it wasn't working for sure? Do you have more then one Remote? Did you try the other?
I know this will sound far out there but may be related to the Door switch that is in the door or drivers door? Even though the car door closes it could be that the switch may not be getting 100% contact
Did work on a 09 the person came in saying they were not able to start the car by remote, Dealer thought could be bad batteries so they replaced them before coming to my shop. I installed a New Aftermarket Alarm RS and a couple of weeks later he came back and said now that one wasn't working...
After looking over his system I found the fault to be bad door switch.
For some strange reason when it was cold the switch in the door just didn't want to work right. Replaced the Switch and the problem went away to the point where I put his aftermarket in Valet Mode, and he didn't have any issues with the OEM RS. However with in a few days he called me up and wanted me to turn the aftermarket one back on because he said and I quote "He had become spoiled with the features the Aftermarket one offered" I told him the steps to turn it back on and has been happy with all since.
Strange thing was that his lights inside went out after closing the door However sometimes his radio didn't turn off when he opened the door. This I didn't know before the new RS was installed and not sure why it was random working and not.
Just thought even though different years maybe something to look at? Only other thing if all things working right in car could be bad module!
So when you try and Remote start the car before it warms up does it take any input from the Remote? Like when you press the Start button does it act like it is going to start but then don't or is there nothing?
Have you tried to lock the doors with the remote a couple of times before you try to start the car?
Next time you try and start your car and it don't work. Please try this! Unlock the car as you normally would, Put the Key in the Ign and turn the key to on. Don't start the car. Wait 10 seconds turn off. Exit and leave the car as you would for the day/night Locking it or what ever you would do. After 30seconds to a Minute try and start the car with the Remote.
Only other issue is that I haven't covered in most OEM RS there a max 2 Start by remote before the system locks out needs to be started by the key before it can start by remote again...
GM OEM RS Fault Issues in No Order.
Coolant temp high or oil pressure low
Car not in Park
Key is in Car
Check Engine Light MIL light is on
Hood Open or unlatched
Low or dead battery in fob
To many Start attempts.
Them are the only ones I can remember there could be more... If you don't get any action after trying to reset the RS by doing the ignition on. Maybe even start the car but don't let it warm up and then try and see if it starts.