I will try to identify the fungus.
I have heard 2 IDs for the fungus that causes rhizome melt. Fussarium and Cylindrocladium. The ID on one of these is second hand but from a source I trust and the other is from a person whose credibility is questionable at times but his account of his collections destruction at the hands of fungus is quite detailed.
Which ever it is there are a few of us growers that are becoming more and more convinced that it is probably a lot more common than most would initially assume. Growers in more northern areas do not see it much but it seems to be almost endemic in the South here in the US. The major trigger for this pest is heat, especially at night. It also seems to be encourages by using the tray method. I am almost certain that the hot, stagnant water provides the perfect conditions for the fungus. Around here (Atlanta, GA) the incidence rates begin to rise when night temps start staying above 25C or so and will spike rapidly when nights are above 28C. Daytime temps over 36C seem to prime conditions as well. Something I personally have noticed (but have not tracked among others) is that a media of peat/sand also seems to encourage growth of the fungus. Small pots also encourage it (media in smaller pots heats faster.)
Once a plant is showing symptoms it pretty much done for. I have saved a few plants but it was extremely difficult and they have never grown well after the recovery effort. If a plant is showing symptoms then the best thing to do is isolate it to prevent spread to other plants in your collection.
Plants with dense/compact growth (purpurea) are quite susceptible as is minor (minor has a predilection for drier conditions in cultivation and most people grow it too wet for its liking.)
The best way to curb the incidence rate of this disease, at least for me, has been the following:
-Pure peat as a media.
-If you are growing in pots, use larger pots (4L or more)
-Top water only with no tray.
-Preferably, grow in micro-bogs or full bog gardens
-I am not going to swear it will work for everyone but for me the use of a beneficial biological has helped. I use one by CustomBio that is a 9 species mix.