MacBook Air shuts down arbitrarily

You don't mention if this happens while the laptop is on the charger or when using the battery only. @anderson1011 is correct that if this only happens when using the battery, then the battery needs to be replaced. Have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate. There is still a slim possibility the battery could cause a problem even when using the charger.

If the issue occurs while using the charger, then we can look for possible software issues. Run EtreCheck and give it "Full Disk Access" so the report includes more details which may provide more clues. Post the report here using the "Additional Text" icon which looks like a piece of paper.

Try running the Apple Diagnostics to see if any hardware issues are detected.

Try an SMC Reset as well.

The amount of charge remaining on the battery is irrelevant. The battery condition is showing as "Service Recommended" which means the battery capacity has dropped below 80% of the original design capacity or macOS has detected a hardware issue with the battery. Either way, you are having issues while running the laptop on battery power only and macOS is saying "Service Recommended". A combination of these two things usually will indicate the battery is at fault for whatever reason.

Coconut Battery can tell you the battery's current Full Charge Capacity in relation to the original Design Capacity in order to see the battery's real capacity remaining. This will be the lower of the two bars in this app.

It can be very difficult to confirm the actual health of the Battery since some issues may only occur when the battery is at a particular charge level.

From everything posted here the battery would be the first thing I would replace. Have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate. Don't install a third party Lithium-ion Battery since the quality of those batteries is extremely poor even when purchased from a respected vendor.

The battery needs to be replaced.