Both my girls have had that problem. The oldest at six doesn't do it much any more, but the four year old does it frequently.
One I won't give her what she wants as long as she's whining. If she won't stop I tell her that babies whine and I won't listen to it. I then send her to her room. I will often imatate her whining...she typically laughs and then I agree that whining looks ridiculous.
The little one I sit for is 2 1/2. She has started to cry when she doesn't get her way and then says she wants her mommy. I remind her that Ms S. doesn't listen to whining from big girls. I explain I have a baby that can't talk and he whines enough for everyone. Then I tell her that if she keeps whining she will have to go sit in time-out.
So here are a few things to think about:
1.) Do you give in? If you give in, then she knows that you have a breaking point and you will give her what she wants.
2.) When you put her in time-out, do you make her sit until she cries. If she doesn't get upset about time-out, then it isn't punishment. The 2 minutes if their 2 is the most ridiculous thing I've ever heard of. Mine have always had to sit until they cry. We talk about why they are going into time-out, if they bug me about getting out, I extend the time-out, and they always sit until I see their eyes starting to tear up. Then we talk about why they are in time-out again.
3.) Try showing her what it looks like when she whines and then follow that up with the right way to ask for what she wants. Repeat it a few times. She will get it.
4.) And seriously if she goes into melt down, then immediately pick her up and take her to her room or a where ever that she's by herself. Tell her that if her tantrum wakes the baby, then she will be punished. In my house that's a spanking...though I know most don't feel comfortable with that.
5.) One more thing...my preacher said something very profound once when he was teaching a series on marriage and the family. He said the things that bug us the most about our kids are typically the things they have learned from us. My girls whine because it's normal for kids to whine at times, but also because they see me whine. I've really started working hard to accept things and set the right example for my girls. I try to maintain an upbeat attitude even when I'm tired. Sometimes I'll tell the girls, "wow mommy sure is tired, but what a beautiful day!"...kinda like yes I feel bad, but I have something to be happy about. I wake them up with a smile, kisses and up beat attitude.
If there is something I want, I will tell the girls, "mommy reallllly would like that, so I'm going to save my money to get it" or "mommy just can't afford that, maybe we can get something else instead"
And I know it's silly, but when I see the girls are really cranky (even the little one I watch)...I'll put in a CD with songs like "Keep on the Sunny Side", "If you're happy and you know it", "You are my sunshine" and we will sing it over and over and over.
My oldest wakes up cranky, so I turn on a light and I gently kiss her and tell her wake-up sunshine. I'll start to gently tickle her and kiss on her. She wakes up with a better attitude.
Oh, and because of my faith and the fact I take my kids to church every week, I will tell them that the devil delights in their sorrow. The Lord wants them to be happy and when they whine the devil does a little jig because they are ruining their testimony. Not sure that will make sense, but it helps especially with the oldest child.
Good days and bad days will always be a part of the territory. Sometimes it's weeks or months that we have to get through, but you will make it. Just be persistent, consistent, insistent, and always set the example.
Good luck!!!