Oh, I feel your pain (or should I say my strop feels your pain). And I've been stropping close to 3 years. It's hard for me to coordinate the flipping of the blade with the back and forth movement. If the blade doesn't flip, the stropping motion continues and that's when you cut it.

My difficulty is a little unique. I throw a ball right-handed and write left-handed. Translated to stropping, I'm naturally right-handed when it comes to moving the blade back and forth, and naturally left-handed when it comes to flipping the blade.

So in my case, to successfully strop I have to flip the blade I have to do it right-handed all the way which is unnatural for me. Doing it left-handed was worse for me.