You gotta create a key for all elements of the character even the one that don't move. So basically on every pose, select the whole character and press S.

But it is better idea to create the run cycle in a stationary position as you mentioned. You can get a way better cycle that way that you can adjust easily and re-use in different scenes. It will also look better cause you're dealing with only limited no. of frames and may tweek it till perfection. Make sure to use a floor-grid when creating the cycle to avoid the moonwalk/feet-sliding effect.