Yes, you just need to learn to ignore it, and eventually it should subside.
Remember, the dog doesn't think he is driving you crazy. He's simply repeating a behavior that was successful in the past.
I read an example recently comparing this to pushing the elevator button and taking the stairs. If we push the button and it doesn't light up, do we immediately go for the stairs? No, we keep pushing the button! We try pushing it harder, faster and longer because experience has taught us that pushing the button works (and we don't want to take the stairs).
So basically, if whining has worked for a while, he's going to whine even more until he finally realizes it no longer works.
Whatever you do, DON'T give in after a long bout of whining, because that will just teach him that he needs to whine for a really long time. Stay strong.