It is normal for plants to "melt" when they change environment. There are a few causes for this, one would be different water parameters. It is likely your water is different from ours and the plant will want to restructure and get it's roots in place to start taking in nutrients. This lag time can cause the plant to consume itself to keep itself alive during the transition. (For more details, read our article on crypt melt.)
Another cause would be a plant converting from emersed (grown out of water) to submerged (growing under water). This happen because the plant farms grow the plants above water in very humid environments. When we get them we start growing them under water. Depending on how long the plant has been in our care will be how much the plant has converted. The plants will always end up finishing this conversion in your home aquarium and would be considered normal.
A lack of sufficient nutrients can also cause plant leaves to start withering away. Make sure you're fertilizing your plants. We recommend using Easy Root Tabs as well as Easy Green Liquid Fertilizer. Without fertilizers, plants will oftentimes die back. For more information, read our article on plant nutrient deficiencies.
Lastly, there is a problem called Anubias rot. This is when the rhizome of an Anubias becomes mushy. This can happen when an Anubias is planted too deeply in substrate and it causes it to rot. This can sometimes be fixed by planting it properly on wood or rock. Then there is another case where the plant may have become damaged and the rot sets in and will consume the entire plant. This can happen at the farm, in our care, during transit, during planting etc. With no specific cause or who is to blame, we offer a refund or a reship of Anubias where this happens when it's been planted correctly and pictures have been provided.
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