Sword plants belong to the genus Echinodorus. All species are marsh or bog plants, amphibious if you like. They can grow emersed or submersed. Many of them spend half the year emersed (the dry season), and half submersed (rainy season). The leaves are different for each; emersed leaves are stronger and constructed to conserve water, whereas the submersed leaves are weaker and designed to let water and nutrients enter the plant.
Echinodorus plants grow from a rosette, with new growth always from the centre. As this occurs, depending upon environmental factors (light and nutrients) the outer older leaves may die off. Provided the new growth is continuing, this is not problematical. These plants also move what are termed mobile nutrients from leaf to leaf. So if nutrients are not sufficient, the plant can move these nutrients to the new growth, and the older leaves slowly yellow. You can leave them attached until the base of the stem is brown, at which point nutrients can no longer move through and the leaf can be removed.
Of course other factors may b involved, I can't tell without a better photo.