Is an object (in this case, God's existence) necessary in this sentence?
We kept discussing.
We kept discussing whether God exists.
For example, with writing, it seems that an object isn't necessary for 'writing'.
I kept writing.
I kept writing my novel.
The answer is that all of your sentences are perfectly valid. Some verbs in English allow multiple valencies, which is to say the number of arguments controlled by the verb. In this case "writing" and "discussing" can both be either transitive, meaning they take an object, or intransitive, meaning they do not take an object.
Valency is a generalization of the concept of transitivity and English has several acceptable valencies. For example, the verb "to read" can take four different valencies:
Read! -- a command to read, avalent.
I read. -- With a subject, monovalent.
I read a book -- with a subject and object, divalent.
I read her a book. -- with one subject and two objects, trivalent.
In the case of "write" and "discuss", only the first three are allowable.
