My 3 year old son has been whining a lot. We make him rephrase and say it in an appropriate voice, but this has been going on for about a month. Are there any other ideas of how to handle this?
You mean besides being consistent and doing your best not to lose patience? :) Even if you are the best parents ever, each child has some growing up they need to do themselves.
The fact that this behavior has lasted a month should not be a concern (except of course that it is really frustrating and wears down your patience I'm sure). The best thing you can do is be consistent and not lost your patience (we all do occasionally, but try to minimize this). If you can do this, it is only a matter of time until your son grows out of this annoying behavior.
As far as specific techniques, you already mentioned a good one--tell them that you don't understand whining and help them to rephrase their statement/request with proper words and proper tone. When they're whining a lot, it may be tempting just to give in occasionally and succumb to their requests/demands just to make the whining stop. This is where your consistency and patience is needed--don't give in!
If your son continues to whine repeatedly over a short period of time (a few minutes), then don't feel obligated to correct every single offense. He may be whining to get attention, in which case acknowledging the whining will reinforce the negative behavior. If after a few attempts to correct his tone your child continues to whine, tell him you're going to ignore him until he can talk like a big boy, and then ignore him. If you're lucky, then he may self-correct at this point. However, it's likely that this will induce tantrums occasionally (how to handle tantrums is a question all on its own!)--you will also need patience so you don't answer his tantrum with a tantrum of your own!
So you have the right idea, just be consistent, be patient, and don't reinforce the behavior by giving in or getting involved in a drawn-out whine session.
When they went through this phase, I told my kids that I'd listen to them once they could say what they wanted without whining. And then I'd ignore whiny requests. All of them. Can't reward bad behavior just because it's more convenient to do so or less embarrassing at a given time.
With one daughter, when she whined, I had a hard time actually understanding what she was saying. So I told her that. And then would wait for her to quit whining. If you're consistent, they'll learn.