I have to deal with PA clients at work all the time and they don't like it when I don't fall for it 
We have a limited supply of audio visual equpiment which books out early on busy weeks. A client rings up, askes for something and I give them the bad news that we don't have anything left. Out come the comments 'Oh no, what will my boss (important person) do now?', 'what a disaster, the event will be ruinied', 'are you sure you don't have anything left for me?', 'But it is for really important person, you can't let me tell them I can't have it, I'll get in trouble!' etc, etc. They great really annoyed when I don't magically find them someting after they pout. I think I've had every PA trick in the book thrown at me and it just doesn't work.
I get this all the time at my PT job (retail) usually involving someone trying to return something past the 90 day deadline, or trying to get some sort of discount where none is available.
I had a customer the other night try and pull the woe is me discount thing. She had put some sale items on hold, and at the time, they were an additional 40% off. But that promo is now over. Also, we technically are only supposed to hold sale items until the end of the day, although if its a customer we know, and know they will be back, we'll do it for longer. Customer had put a number of items on hold maybe a week ago, while the extra % was still on. But when she came in, that promo was over, and they were "as marked" she bemoaned the fact, and went on about how she had ONLY put them on hold since it was an extra % off.
Well, sorry, but a. if it was that important you got the extra off, you should have come in, or at the very least, which we can also do, called and paid for them on the phone and b. i am not losing my job to give you a discount that doesn't exist or that you are not entitled to.
I've gotten very good at not JADE-ing, and simply telling them I'm sorry I can't do what you want, or comiserating about their "bad luck" (i.e. not purchasing when it was a better deal) Then I simply stop talking.