Frost Free Valve Problem

I have a Mansfield frost free valve that is sqeeking when the valve is turned. I want to lubricate the valve parts with faucet grease.
The problem I'm having is removing the white "plastic" nut which holds the stem of the valve (not the grey valve knob). I have tried to turn it clockwise and counter-clockwise but it refuses to move. I sure don't want to break it and have to replace the valve.
Any ideas?

Use penetrating oil surrounding where it connects into the valve; it will come apart in due time just be patient and you can use grease on the moving shaft.