I've found that slugs and snails LOVE Ludisia so it's possible that the slimy buggers are the culprits.
Ludisia typically roots very easily from cuttings. Simply remove any necrotic tissue, and dust the cut end with some sort of antifungal powder (cinamon generally works well or rooting hormone) and stick the cutting(s) in a lightly moist -- not wet -- mix. I've used a peat, bark, & perlite/hydroton/charcoal mix before. I have heard of folks rooting them in water but personally have never done so. Bury the cutting so one or more root nodes are covered.