Failure to pitcher is usually a result of low light and humidity. But clearly you have bigger troubles than no pitchers!!!
The plant next to it appears to have the same thing, but the new growth is unaffected. Does this happen from the roots up? If so, we may be looking at a fungus of some sort. Neem oil is my go-to antifungal treatment (it is also an excellent pesticide, as well, incase this is from an insect).
You should also take a look at your soil, how old and broken down is it? Nepenthes like an airy, well-draining mix.
The vining plant pictured appears to have a basal that seems fairly healthy, so my final suggestion to you is this: Cut off the vine, throw it away. Check the soil, repot if necessary. Spray the remaining basal with Neem or some other fungicide/insecticide. Look into increasing the light and humidity around the plant.
This is an excellent resource if you have further questions about your Nepenthes:
Terra Forums Carnivorous Plant Discussions