MacBook Air battery does not hold a charge when powered off

Batteries are considered Consumable Products. Over time it will degrade to a point where it needs to be replaced. The usage is normal as the capacity will go up and down all the time and never stay always at 100%. Apple Batteries are rated for 1000 Full Battery Cycles and / or 80% Capacity before needing Evaluation or replacement.

For additional reading on Battery and Apple Computers this link may help. About battery health management in Mac notebooks and especially for the M1 and Big Sur If battery charging is paused or on hold on your Mac

A feature introduced into Big Sur was to preserve the number of Full Battery Cycles - there was an Algorithm coded into the macOS. It is perfectly Normal for Big Sur to Pause / Suspend charging the battery beyond 80% and hold it at that level. One can nudge / over-ride this by clicking the Battery Icon on Desktop Top Bar and allow charging beyond 80%. From observations, it will Pause / Suspend again once reading 90%. Same procedure to over-ride and will charge to 100%

All batteries can suffer from "self discharge" especially rechargeable batteries.

This phenomenon also tends to increase as the battery ages due to

both recharge cycles and simply age and also storage temperatures.

Also, even though the computer is "off", there is still a small amount of power

being drawn from the batteries to maintain certain functions.

Without knowing precisely which model MacBook Air you have it is hard to

say if this can be expected behavior or not.