I found this when playing Skyrim on my 5870 too but remember - just because the memory is maxed out doesn't necessarily mean the game will be unplayable. The card will have some form of memory management.
As the VRAM usage approaches a threshold, less-used textures will be dropped off. This does cause extra work for the card, especially if the textures need to be brought back from the regular RAM over PCIE to the card.
When I changed my 5870 1Gb for a 7950 3Gb I found that on exactly the same settings and textures, Skyrim was actually using just over 2Gb of VRAM. It obviously didn't have to swap the textures in and out of VRAM any more and so the framerate was steadier. As a result I was able to increase the detail levels and even look at ENB visual effects. Currently I am still able to play the game at a fairly steady 60fps at 1440p with about 2.4Gb reported as used on the card.