By “stall out” I assume you mean the engine, which started and was running, dies. The battery is not a suspect for this symptom.
If it never happens going forward, it’s very likely related to engine movement. The engine rocks a bit on its mounts when under load–in one direction when going forward, and in the other direction when going backward. I would guess that when it rocks in the direction associated with reverse, something that is worn in some way is getting yanked and causing the dying.
If the motor mounts are worn/broken, this engine movement will be exaggerated and it would be a good idea to replace the worn mount(s). Badly worn mounts might even have caused the problem. But worn mounts by themselves won’t cause the car to die.
A very likely suspect on many cars is the air intake duct between the air filter and the throttle body. (This is assuming the car has an airflow sensor next to the air filter.) This duct is usually 3 or 4 inches in diameter, made of a stiff rubber. Typically the duct will have a tear/crack in it, which opens into a gap when pulled in one direction. A temporary fix can be made with duct tape; the reliable fix is to replace the duct, which is not terribly expensive (I’d guess under $100 installed).
Another possibility is a wiring connector or harness separating or shorting out when it’s pulled on. In a case like this, it would be necessary to identify just where the problem wiring is, and then repair it.
I would say it has something to do with your idle setting. When cars are warm they usually run better. When theyre cold they need more input from the computer to get/stay running. Since you use reverse mostly when the engine is cold the stalling problem will show up when you put the car in reverse and load the engine. I bet you dont have a stalling problem in reverse after the car has had time to warm up. The reason you may not notice it when its cold and you put it in drive (as opposed to reverse) is you can usually just give it gas and go. When you back up you`re easier on the gas pedal. I would have the cold idle setting checked.
I think whuckfistle has it nailed. It’s not a problem that can’t be overcome. It’s just annoying. I will ask the mechanic about how much trouble it is to get that fixed.
I could also be a bad sparkplug wire, causing a weak spark. Once the engine is going good, not as much is needed to cause the explosion. A bad sparkplug could cause it as well.
Idle used to be a common problem with carborated cars. Now that everything is injected, it’s actually rather uncommon.
Only on older engines. On anything new the idle is controlled by a computer and turning screws only tends to confuse the computer and make things worse.
If the problem is worse when it’s cold and damp (only cold was mentioned), then my vote would be on the ignition system, most likely the spark plug wires simply need replacing.