Have you explored all the different options for BIF on the 7D? Things like AI servo tracking sensitivity, Servo tracking priority, Servo tracking method, as well as the AF options like single point expansion and Zone AF?
I find Zone AF coupled with a fast tracking sensitivity makes BIF ridiculously easy and you have a block of nine focus points to keep the bird locked-on For more precision capture/tracking of single birds then I use single point expansion with a slow Servo tracking sensitivity, that way if you lose the bird it gives you plenty of time to get back on without the AF going wildly out and locking on to something in the background. I must admit I find all these things are a lot easier for BIF if you also use back button focusing as well.
While the more modern Cameras like the 1D3/4 are probably better than the 7D for BIF (although a lot of people argue that the 7D is better than the 1D3 in this department!) I would have doubted that the older 1D2 would have been so good but having never used one I stand to be corrected.