I understand that the word 立つ has various meanings, but basically can be used to describe a state (for inanimate and animate objects) as well as a process (for animate objects). To describe a state for inanimate objects both: 立つ and 立っている seem to be accepted forms (ビルが立つ, ビルが立っている).
Now, an idiomatic expression 顔が立つ is undoubtedly used to describe a state of "keeping one's face".
The form 顔が立っている does not seem to be recognised. is my observation wrong?
What exactly does 立つ mean in this context and why the form 立っている is incorrect? Is it really a state, or could it be a response to some kind of a ..."periodic test"? Like "whenever I look at him, his response is 顔が立つ thus he is a man of honour"?
If the form 顔が立っている is incorrect, how does 立つ in 顔が立つ differ from 立つ in 腹が立つ, where 腹が立っている is also recognised and used form?