I'll take a stab at this, but remember I'm a Navy guy and not involved in Aviation. So this is really not my cup of tea.
As has been said, we don't really have the tech.
We have something for Naval vessels that's kind of similar to what you're asking for:
http://en.wikipedia.org/wiki/CIWS
But keep in mind, an RPG is much smaller than a missile (obviously), so detection would likely be more difficult (read the article for the limitations on this system).
Also, this is obviously too big and heavy for a helicopter.
Lastly, regarding budget. We are stretched much thinner than you realize. It's already been said before, but I'll give you some more specific information. Right now our manning on our Naval ships is averaging around 60%. This means on a ship designed for a crew of say, 500, we're operating with 300 (not actual numbers. I have them, but don't want to post on a public forum). Not only that, but the Navy is being more and more strict about their recruiting requirements, and about their re-enlistment requirements, in order to further shrink our overall manpower. We simply do not have the budget to even pay our existing undermanned workforce.
In addition, a good portion of the equipment on our ships were designed as much as 50 years ago. For example, if you saw some of the computer equipment on board my ship, you would be shocked. The computer that runs our missile launcher system, is significantly less powerful than the pc or laptop you're using to read this post. I'll take that a step further. Flash back 15 years ago. Our launcher computer is less powerful than the computer you used to play BASIC games like Snake on. Obviously, there's better technology out there, and many of the newer ships are being fitted with it, and the older systems are being revamped slowly, but we literally do not have the budget to afford it. So trust me. Our budget is being stretched very thin. We're not just sitting on money.
If you choose not to decide, you still have made a choice.
Lassev: I guess there was something captivating in savagery, because I liked it.