One of the biggest reasons people get off plane is that they let their hands move 'out' on the backswing, usually right off the bat - rather than the hands going back, up and in.
This results in a 'lift and roll' move where the hands are too far outside, above plane, while the clubshaft and clubhead are likely too inside and underplane (visually).
Practice your takeaway with the shaft along a picnic bench, which will let you 'allow' the clubface rotation and still stay on plane - tracing a straight plane line
This is a super old post but just wanted to say thanks. I thought I was on plane until I read this. It has helped my ball striking. Just like EdZ said, I was right off plane from the start!!