1) Not enough light. This probably the most common. The standard tank hood does not provide enough light for most plants. You must either upgrade your lighting, or choose your plants carefully.
2) The plant is not really meant to grow underwater. Many of the plants sold as aquarium plants won't live long submerged in an aquarium. They'll do all right for a few weeks or months, but eventually die. See the Krib's plant blacklist.
3) Death of the emersed growth. Nurseries often grow even true aquatic plants "emersed." That is, the roots are underwater, but the leaves are above the surface. This keeps algae and snails off the leaves, and the plant grows faster and produces tougher leaves that stand up to shipping better. But when you put the plant underwater, the emersed leaves slowly die. If the plant is a true aquatic, new, submersed leaves will grow in (often looking quite different from the emersed ones). You just have to be patient.
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