Hi Naoki,
Gin posed a good question..."is the brown part soft?"
If it is...and I suspect it might be because you mentioned the leaves died and it looked like they had a rot...I would cut the top of the plant off.
Make sure that your cut is clean and no brown is showing in the exposed stem. If there is brown showing, clean your cutting tool and remove an additional 1/2 inch of stem. Do this until you have a clean looking exposed stem section. At this point, you can treat it with a good systemic fungicide like Diathane M-45. I would make a paste from the fungicide powder and brush it on the exposed stem. Your plant will do fine, and the keikis should grow quickly. I've had to do this to a few of my vandaceous plants over the years and have had good results.
Of course, if the brown part is not a rot, just follow Gin's suggestion.
i hope this helps.