But, she added, "it is likely to fail."The answer depends on whether you want the "but" to go with the quote or with the fact that the person is saying such a thing. The difference between those two choices is generally too subtle to worry about, but it is important to avoid a mixed bag in your punctuation. A comma before the attribution indicates that the "But" is part of the thought being attributed, and so the quote, being a continuation of that thought, should not be capitalized as though it were the beginning of a sentence.
If the "But" is meant to apply to the "she added" part, a quote that is a complete sentence should be capitalized like a complete sentence:
But she added, "It is likely to fail."These little markers can be obscured, of course, if the quotation begins with a proper noun or if you have avoided or overcome any lingering trauma from the Strunkwhite caution on beginning a sentence with "However":
However, she added, "John is like to fail."In that case, you could emphasize that "However" isn't being put in the speaker's mouth by using a colon instead of a comma to introduce the quote.