Are Buddhist prayer flags taken down once the prayer has been answered?

The question uses prayer in the Christian sense - a request to the Christian God for intercession or a favor.

The Tibetan prayer flags are colored strips of cloth with mantras written on them (e.g. Om Mani Padme Hum) which are posted so that the peace of the mantra can be spread by the wind to the world - think of a cloth covered with perfume being hung up so the wind would carry the sweet smell to the world.

As consequence the flags are neither put up when a favor is required, or taken down when a prayer is acted on. Rather they are put up and allowed to blow away until faded and eroded to nothing by the sun and wind.

Aside: Prayer flags are unknown in Buddhism outside of Tibet. They are believed to have originated with Bön, an ancient religion which predated the coming of Buddhism to Tibet.