How to fix a broken pan sauce?
I made a roast chicken last night, and like I always do I made a pan sauce from the browned vegetable bits and drippings at the bottom of the pan. I did what I normally do: poured off all but a tablespoon or so of fat, set in on medium high heat, added 1/4 cup dry vermouth and cooked that until very reduced, about 5 minutes, then added 3/4 cup of stock (one thing I did differently last night was subbed 1/4 of the stock for unfiltered apple juice, but I wouldn't think that would matter), let that reduce by half, about another 7 minutes, and then added two tablespoons butter and 1 teaspoon cornstarch and whisked it until it looked emulsified and satin-y, then turned off the heat. The sauce that had been incorporated then just fell apart, and separated in the most spectacular fashion I've ever seen. Just a pile of oil and browned solids, it was super depressing. The only thing, other than the apple juice, that was different from previous times is that my heat may have been a little higher throughout the process. So, my question is twofold: 1) what caused my sauce break? and 2) is there any way to repair it once it's broken?