I have the same problem with the axis of a thread.
I have to tell you that I have designed a different layer for thread and made the settings to add the thread features there, therefor when I add a thread is going automatically on both layers (axis and thread), so after that I remove the thread feature from axis layer, and than I add only the label of axis into the axis layer with: Layer/add item/text and I select the name of axis.
In this way the name of axis can be hide but the line of axis remains visible. It is a compromise that I think can be accepted. Ore interesting think is if you make a copy of the thread feature (by copy/mirror for example),than the axis is not visible at all on the copy feature.
I use ProE2001 but as far as I know it is the same problem in Wildfire.