Is there any reason to use the subjunctive mood in the question "If I asked, would she say it were/was time?" There's an air of uncertainty about "were" when compared to the past tense "was," but is it grammatical to use the subjunctive? Archaic?
Fowler says the past simple is used in clauses that depend on a clause in the past subjunctive, so it should be was. I and almost everyone, I believe, will agree with this advice. There is no specific reason why this is so: in fact, the past subjunctive is possible or even compulsory there in other languages, or even in older English. I don't have the quotation on hand at the moment, but I'll try to find it.
No, in fact the subjunctive "were" is not possible here. I don't know why. I can't think of an example in modern English where subjunctive "were" can be used in the "then" clause of an if-then construction. But in older English, we have Macbeth saying "If it were done when 'tis done, then 'twere well it were done quickly."
"If I asked, would she say it were/was time?"
9h. The subjunctive were is used in contrary-to-fact statements (after if or as though) and in statements expressing a wish.--Warriner's.
To create the subjunctive mood, you would have to change your sentence to: "If I were to ask, would she say it was time?"
John E. Warriner. Warriner’s English Grammar and Composition. Fifth Course. Liberty Edition. Orlando, Florida: Harcourt, Brace, and Jovanovich. 1986. 208.