My MacBook Air just shuts down when idle for a brief minute

I would clear and reset everything, start with the PRAM.

then run first aid in disk utilities and repair any issues.

you could have a program like a video one that hampers the MacBook air where it shuts down.

My MacBook air from 2010 shut down after trying to export a 10 min video from an iPad.

i hope this helped!

You mentioned Shutdown. Usually if the computer suddenly shutdown there is an Error Message pop-up on the screen when starting up and logging into the computer. Is that what is happening?

If you mean goes to Sleep and have to wake it up that is something else