With maintenance or flying of about 11 or so turbine types none of them have liked tailwind starts and on one or two of them it was a recipe for cooking the hot end……… don’t do it !
Some airliners even have a procedure for deploying the thrust reverser before start if you must start in more than x knots of tailwind. Saves an auto shutdown during start or, worse still, a hot start.
Nxi upgrade solved the problem: since then no weak battery anymore.
The electric power required by the legacy G1000 was apparently the main cause for weak battery.
Neither Textron nor Garmin told about that in their sales pitch for upgrade.