By "die" what exactly do we mean? That the system is being discontinued, has stopped being supported, or no longer has new games?
I think the PS4 and One will each have their successors come out in 2020, and will be supported with major releases including both multiplatform and exclusive titles until 2022. As for when they're discontinued... no sooner than 2023, and as late as 2028, depending on how well they do.
As for the Wii U, I expect Nintendo to be unable to make a successor ready until late 2018 or so. Then, the console will likely be discontinued and stop receiving games by early 2020, assuming the system continues to do poorly.
The 3DS will likely be succeeded in late 2017, give or take up to a year depending on how well the system does in the future. Considering how the DS STILL gets new games, I expect the 3DS to get new titles, if only for the eShop, at least as late as 2020.
The Vita is a mystery to me, simply because it's the only system that has a good reason to be discontinued. Assuming Sony wants to make a third handheld, the Vita can be replaced as soon as 2016, with support in most of the world vanishing within a year. However, Japan might very well adopt the Vita like the PSP before it, which would extend the system's life by as much as a couple of years.