I am guessing your main plant is a Hylocereus. That's what they usually use for grafting. It should be done in very sterile environment as open exposed areas of the host plant can get fungus and bacteria in the open areas. So once your grafted plant falls off to the soil it is contaminated. Once fungus get's into the main system of the plant, I don't think there is any hope for the little plant. They seem to dissolve from within. Grafting is done because the plant being added, usually a very week and slow growing that can take on these diseases. Now the main plant, usually Hylocereus undatus is a strong fast growing vine. That's what is left of yours. Some people support the plant like a vine and some others let them grow along the ground. The segments can easily be broken off the planted and will readily root and do well.
waretrop> Thank you! This information is really useful. Everything happened almost as like you written. As soon as the yellow one fell off, green one seems to be very happy and growing fast. I guess I won't do grafting, since I am too afraid do do something very wrong, but I am happy about green one.
I don't know how long you have had the plant, but maybe, I'm thinking, it never really took and didn't get rooted on it's intended host. Another thing may have happened is that, it got banged or knocked, which to allow air born fungus or something to grow between the two. It looks like the original plant has scared over very well so I don't think it is in jeopardy. Plus the bottom plant has much more stamina than the one being placed on top. That's one reason that they use it.
