Sheets that were bright white when you bought them gradually turning grey or yellowish is a very common problem, but one that is usually misdiagnosed. Most people look for the answer in more detergent or bleach. The situation often calls for exactly the opposite.
The main cause of greying is dirt from the wash water settling back onto the fabric. If the machine is overloaded, if there is too little or too much detergent, or if whites are washed with colours, dirt cannot stay suspended in the water and goes back onto the fibres. Hard water makes this easier.
Yellowing is usually a different story. Body oils and sweat oxidise in the fibres over time. And there is bleach: with some synthetic fibres, and where the water contains iron, chlorine can turn fabric yellow instead of whitening it. A more effective approach is to wash whites separately with the right amount of detergent, use an oxygen-based bleach now and then, and dry them in the sun when possible. The sun is the oldest and gentlest whitener.