I can't find it documented in the version 8 docs, but I did find it in my copy of Jump Into JMP Scripting (Murphrey and Lucas) which I recommend. If you have previously added a reference line to an axis at, say, 100, then send the axis box the message: Remove Ref Line( 100 ).
From the same resource, in versions prior to version 8 the trick is to send the axis box the message to add a new solid reference line at the same location with a color slightly different from the background. If you make it exactly the same as the background JMP will change the reference line color to something visible against the background.