How's it doing? It is so small are you sure it isn't under-potted? A few months ago there was a long discussion on the Houseplant Forum about this type of growth. If you find the site it's worth reading.

Mine did the same thing...all leaves are gone now but the center stem is firm...I think mine had travel/transplant shock, sensitive to temp change and being moved...

I have a plant of the closely related Begonia partita and it sheds like a sheepdog. Shedding leaves seems to be common behavior with the varieties of Begonia Dregei. I don't think it likes drying out as much as the descriptions say. I planted mine into a well drained cactus type soil and water often and It seems happier. It still blooms up a storm and drops lots of spent blossoms, so keep it an easy plc to reach and clean.