Try resetting SMC first and only after a SMC reset did not solve your problem you should think about replacing your battery. Start inspecting all the different components involved. Your MBA will now be able to hold a charge like it did when new. Make sure you note where each screw comes from as they are different. Don't yank it off, use a spudger or similar tool to disconnect the molex connector by 'wedging' it off. Just be careful when disconnecting the battery from the logic board. Then, just remove the screws holding in the battery and swap. Just remove the screws holding the back cover in place. To replace the battery it's actually very simple. Definitely avoid the ones with less than a 12 month warranty no matter how inexpensive they are. From personal experience, the more 'warranted' batteries lasted much longer. You just need a new replacement battery battery (I suggest getting ones with at minimum a 12 month warranty 18 month is better). If we unplug the power adapter, the battery has nothing to supply so the computer shuts off. (Coincidentally, I have a MBP with the exact same symptoms you have, so the output here works perfectly!) The key here is that under 'Amperage' we get a '0' which means there is literally no current coming from the battery (Note: even though it may have voltage, if there are no amps, it won't have the 'power' to supply).

Here we can see that the battery is in need of service. You can limit it to just the battery info by tweaking the command as follows: $ system_profiler SPPowerDataType | grep -i 'charge information' -A 10 The output can be rather lengthy the info you need will be at the top. That will give you all the power settings related to your Mac. Using Terminal, just issue the command: $ system_profiler SPPowerDataType These are all good, but in my opinion, I would much rather use built in tools to get this info. There are a number of utilities that you can get (paid and free) that will look at your battery status:

If it's necessary to have the power adapter plugged in when trying to turn it on, it's a sure sign that the battery is discharged.

The computer (in this case your MacBook Air) turns off because there is no more/not enough charge in the battery.

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