According to the docs for TextInput it supports the same styling options as Text. In testing this at the bare minimum all of the shadow and line decoration options aren't supported.

This can be seen in this playground:
https://rnplay.org/apps/sdqbqw
If the Text element is replaced with a TextInput element with the same style the shadow is lost.

I can imagine that the native text input element isn't conducive to supporting shadows, which is why this is happening.