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When this happens does it feel like the engine is being drug down, like if you left a manual trans in gear, held the brake and let out on the clutch? If that's what it feels like then your torque converter clutch is most likely turning on when you put it in gear. In the front of the converter there is a disc clutch that turns on at certain times to give a mechanical lock between the engine and trans to lower engine RPM's. Usually this doesn't just happen in reverse but it's possible.
If it doesn't feel like it's being drug down then I would either try to have a look at some data or set up a spark tester on it as it dies. If it dies abruptly then you are losing spark, if it hesitates and runs out of power that's a sign you are losing fuel. It's possible that the powertrain shift that happens when you put it in reverse is causing a wire to rub through to ground or is causing an intermittent open circuit and this is taking down spark, fuel or both.
It only does it in reverse, I can pass reverse into drive and drive it all day long at any speed so it does not sound like a clutch problem.
Why would it not lose fuel or spark in other gears?