"We had a good time despite its raining."
Why does the genitive pronoun not work here, yet in the majority of examples we have a choice between accusative and genitive pronouns:-
We had a good time despite him being ill. OK
We had a good time despite his being ill. OK
We had a good time despite them arguing. OK
We had a good time despite their arguing. OK
We had a good time despite it raining. OK
We had a good time despite its raining. NOT OK.
And what exactly is "it"?
Also am I correct in thinking that their arguing is a noun phrase, whereas them arguing is a non-finite subordinate clause? And if that is true then with a sentence like "We had a good time despite arguing" what is despite arguing? Is it an NP or a non-finite clause? Or is it a Schroedinger's cat?