Even with frequent washing, perspiration can build up in clothing under the arms and around the collar. This is especially true in homes served by hard water. The more minerals in the water, the harder it is to get stubborn residues out in the wash. Undissolved deodorants are often the culprits that contribute to the stains, so don't feel bad -- your underarm stains may not be your fault!
To help remove perspiration stains on light-colored clothing, make a baking soda and water paste and paint it onto the stains with an old paintbrush. Let it sit for an hour or more, then launder as usual. If stains persist, apply the baking soda paste again, but try painting on a bit of undiluted vinegar first.