Just a thought -

It's simply not in their interests to do so. They're not terribly worried that Iran will lob a nuke into their backyard. Iran knows that the odds of Russia retaliating to a major terrorist MWD strike with a nuke is FAR higher than the odds of us doing so. A missile shield doesn't buy them much new protection at all.

They also know that from the standpoint of an all-out nuclear exchange, we'd probably benefit more from a missile shield than they would because we can afford to build more nukes than they can. Putin cannot afford to engage in an arms build-up like the one which ultimately helped crush the Soviet economy in the late 1980s. With current technology, a missile shield will have a decent chance at stopping one or two rogue missiles, but will not be able to stop dozens coming through at once. Thus if, God forbid, there were ever a mass exchange of nukes, more of ours would be more likely to make it through their shield, simply because we'd have more. Not to mention that the shield itself will probably be very pricey, and they may not be able to afford to take part in it.

Beyond that, Russia has no interest in partnering with America against any other part of the world. From their point of view, such partnerships come with way too many strings attached, and anyway they are tired of not being seen (and feared) as a superpower any more. They'll oppose us on some thing just for the sake of opposing us.