Is thermal radiation lost to air

I get the feeling that this should be obvious, and I feel embarrassed because I do actually have some education in Physics, but I have no idea. All objects radiate heat. This heat is transferred to other matter. Air is matter, so thermal radiation should affect the air as well - and obviously, any heat absorbed by air can't also heat other objects (conservation of energy).

Is thermal radiation 'lost' to air? Is this effect negligible for most practical calculations?

Except on certain conditions of atmosphere, almost all thermal energy is transmitted through air without heating the air. Earth absorbs this energy and emits as infra red radiation to the atmosphere.
Now this energy is absorbed by air in the atmosphere.
The absorbed energy is remitted in all directions by the air, the radiations sent upward are lost , whereas sent downward are again absorbed by earth.
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Nothing is lost.If the air is cool with respect to the radiating body then convection currents will be formed and as soon as so rounding air temp and object temp becomes equal heat exchange will stop ie they will reach thermal equilibrium.

Ar is mostly transparent to infrared radiation.