48fps was chosen because it was compatible with a certain type of 3D projector that most digital theaters had used. Thus theaters didn't need to invest in an entirely new projector just to show the HFR version. The IMAX-certified 3D projectors (note: not IMAX domes) that RealD was pushing around the time Avatar came out was capable of this.

Technically, I think those projectors can go up to 60fps in 3D, but I can't remember/easily find where I read it so I'm not that confident about that figure.